Three-dimensional display apparatus, three-dimensional display system, head up display, head up display system, three-dimensional display apparatus design method, and mobile object

ABSTRACT

A three-dimensional display apparatus  3  comprises a display panel  5  (display element) and a parallax barrier  6  (optical element). The display panel  5  displays a left-eye image and a right-eye image respectively in first subpixels  11 L and second subpixels  11 R. The parallax barrier  6  transmits at least part of the left-eye image toward the left eye, and at least part of the right-eye image toward the right eye. A first sertain number of the first subpixels  11 L and of the second subpixels  11 R are each successively arranged in each column. A region in which the first subpixels  11 L are arranged and a region in which the second subpixels  11 R are arranged are displaced from each other by a second sertain number between two adjacent columns. The first sertain number is greater than the second sertain number and is not a multiple of the second sertain number.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority to and the benefit of Japanese PatentApplication No. 2017-210105 filed on Oct. 31, 2017, Japanese PatentApplication No. 2017-013685 filed on Jan. 27, 2017, Japanese PatentApplication No. 2017-013686 filed on Jan. 27, 2017, and Japanese PatentApplication No. 2017-013687 filed on Jan. 27, 2017, the entiredisclosures of which are incorporated herein by reference.

TECHNICAL FIELD

The present disclosure relates to a three-dimensional display apparatus,a three-dimensional display system, a head up display, a head up displaysystem, a three-dimensional display apparatus design method, and amobile object.

BACKGROUND

Display apparatuses including barriers for causing different image lightto reach the left and right eyes of a user to provide stereoscopicvision without the aid of special glasses and the like areconventionally known (e.g. PTL 1, PTL 2, and PTL 3).

CITATION LIST Patent Literature

PTL 1: US 2015/0362740 A1

PTL 2: JP 2001-166259 A

PTL 3: JP H9-50019 A

SUMMARY Technical Problem

Conventional three-dimensional display apparatuses have room forimprovement in techniques of appropriately displaying athree-dimensional image to the left and right eyes.

It could therefore be helpful to provide a three-dimensional displayapparatus, a three-dimensional display system, a head up display, a headup display system, a three-dimensional display apparatus design method,and a mobile object having improved techniques of appropriatelydisplaying a three-dimensional image to enhance convenience.

Solution to Problem

To achieve the object stated above, a three-dimensional displayapparatus according to an embodiment of the present disclosure comprisesa display apparatus and an optical element. The display apparatus has adisplay surface including subpixels arranged in a grid in a firstdirection corresponding to a direction in which parallax is provided toeyes of a user and a second direction approximately orthogonal to thefirst direction, and is configured to display a left-eye image and aright-eye image respectively in first subpixels and second subpixelsseparated by display boundaries passing along boundaries between thesubpixels. The optical element is configured to selectively transmit atleast part of the left-eye image in a direction of an optical pathtoward a left eye of the user, and selectively transmit at least part ofthe right-eye image in a direction of an optical path toward a right eyeof the user. When an arrangement in the first direction of the gridformed by the subpixels is a row and an arrangement in the seconddirection of the grid is a column, a first sertain number of the firstsubpixels and of the second subpixels are each successively arranged ineach column. A region in which the first subpixels are arranged and aregion in which the second subpixels are arranged are displaced fromeach other in the second direction by a second sertain number betweentwo adjacent columns. The first sertain number is greater than thesecond sertain number and is not a multiple of the second sertain number

To achieve the object stated above, a three-dimensional display systemaccording to an embodiment of the present disclosure comprises a displayapparatus, an optical element, a detection apparatus, and a controller.The display apparatus has a display surface including subpixels arrangedin a grid in a first direction corresponding to a direction in whichparallax is provided to eyes of a user and a second directionapproximately orthogonal to the first direction, and is configured todisplay a left-eye image and a right-eye image respectively in firstsubpixels and second subpixels separated by display boundaries passingalong boundaries between the subpixels. The optical element isconfigured to selectively transmit at least part of the left-eye imagein a direction of an optical path toward a left eye of the user, andselectively transmit at least part of the right-eye image in a directionof an optical path toward a right eye of the user. The detectionapparatus is configured to detect positions of the left eye and theright eye of the user. The controller is configured to move the displayboundaries, based on the positions of the left eye and the right eye ofthe user detected by the detection apparatus. When an arrangement in thefirst direction of the grid formed by the subpixels is a row and anarrangement in the second direction of the grid is a column, a firstsertain number of the first subpixels and of the second subpixels areeach successively arranged in each column. A region in which the firstsubpixels are arranged and a region in which the second subpixels arearranged are displaced from each other in the second direction by asecond sertain number between two adjacent columns. The first sertainnumber is greater than the second sertain number and is not a multipleof the second sertain number

To achieve the object stated above, a head up display according to anembodiment of the present disclosure comprises a display apparatus, anoptical element, a detection apparatus, a controller, and an opticalsystem. The display apparatus has a display surface including subpixelsarranged in a grid in a first direction corresponding to a direction inwhich parallax is provided to eyes of a user and a second directionapproximately orthogonal to the first direction, and is configured todisplay a left-eye image and a right-eye image respectively in firstsubpixels and second subpixels separated by display boundaries passingalong boundaries between the subpixels. The optical element isconfigured to selectively transmit at least part of the left-eye imagein a direction of an optical path toward a left eye of the user, andselectively transmit at least part of the right-eye image in a directionof an optical path toward a right eye of the user. The detectionapparatus is configured to detect positions of the left eye and theright eye of the user. The controller is configured to move the displayboundaries, based on the positions of the left eye and the right eye ofthe user detected by the detection apparatus. The optical system isconfigured to project image light emitted from the display surface andtransmitted through the optical element so as to form a virtual image ina field of view of the user. When an arrangement in the first directionof the grid formed by the subpixels is a row and an arrangement in thesecond direction of the grid is a column, a first sertain number of thefirst subpixels and of the second subpixels are each successivelyarranged in each column. A region in which the first subpixels arearranged and a region in which the second subpixels are arranged aredisplaced from each other in the second direction by a second sertainnumber between two adjacent columns. The first sertain number is greaterthan the second sertain number and is not a multiple of the secondsertain number

To achieve the object stated above, a three-dimensional displayapparatus design method according to an embodiment of the presentdisclosure is a three-dimensional display apparatus design method for athree-dimensional display apparatus including a display apparatus and anoptical element. The display apparatus has a display surface includingsubpixels arranged in a grid in a first direction corresponding to adirection in which parallax is provided to eyes of a user and a seconddirection approximately orthogonal to the first direction, and isconfigured to display a left-eye image and a right-eye imagerespectively in first subpixels and second subpixels separated bydisplay boundaries passing along boundaries between the subpixels. Theoptical element is configured to selectively transmit at least part ofthe left-eye image in a direction of an optical path toward a left eyeof the user, and selectively transmit at least part of the right-eyeimage in a direction of an optical path toward a right eye of the user.The three-dimensional display apparatus design method comprises:determining a optimum viewing distance; determining an image pitch thatis a pitch in the first direction with which the left-eye image and theright-eye image are displayed, based on the optimum viewing distance;determining a first sertain number and a second sertain number based onthe image pitch, the first sertain number being greater than the secondsertain number; and determining an arrangement method of the firstsubpixels and the second subpixels and a shape of the optical elementbased on the first sertain number and the second sertain number. When anarrangement in the first direction of the grid formed by the subpixelsis a row and an arrangement in the second direction of the grid is acolumn, the first sertain number of the first subpixels and of thesecond subpixels are each successively arranged in each column. A regionin which the first subpixels are arranged and a region in which thesecond subpixels are arranged are displaced from each other in thesecond direction by the second sertain number between two adjacentcolumns

A three-dimensional display apparatus according to an embodiment of thepresent disclosure comprises a display surface and an optical element.The display surface includes subpixels arranged in a grid along ahorizontal direction and a vertical direction. The optical element isconfigured to define, for each of strip regions extending in a sertaindirection on the display surface, a light ray direction of image lightemitted from subpixels. An edge of each of the strip regions traversesthe subpixels, and a length of a one pixel section of the edge along thehorizontal direction is shorter than a length of the one pixel sectionof the edge along the vertical direction

A three-dimensional display system according to an embodiment of thepresent disclosure comprises a display surface, an optical element, acamera, and a controller. The display surface includes subpixelsarranged in a grid along a horizontal direction and a verticaldirection. The optical element is configured to: define, for each ofstrip regions extending in a sertain direction on the display surface, alight ray direction of image light emitted from subpixels, wherein anedge of each of the strip regions traverses the subpixels, and a lengthof a one pixel section of the edge along the horizontal direction isshorter than a length of the one pixel section of the edge along thevertical direction; and cause light emitted from subpixels in part ofthe strip regions to propagate to a position of a right eye of a user,and light emitted from subpixels in other part of the strip regions topropagate to a position of a left eye of the user. The camera isconfigured to capture an image of the right eye and the left eye of theuser. The controller is configured to determine three-dimensionalpositions of the right eye and the left eye of the user based on theimage captured by the camera, and control an image displayed on thedisplay surface based on the three-dimensional positions of the righteye and the left eye.

A head up display system according to an embodiment of the presentdisclosure comprises a display surface, an optical element, a camera, acontroller, and an optical system. The display surface includessubpixels arranged in a grid along a horizontal direction and a verticaldirection. The optical element is configured to: define, for each ofstrip regions extending in a sertain direction on the display surface, alight ray direction of image light emitted from subpixels, wherein anedge of each of the strip regions traverses the subpixels, and a lengthof a one pixel section of the edge along the horizontal direction isshorter than a length of the one pixel section of the edge along thevertical direction; and cause light emitted from subpixels in part ofthe strip regions to propagate to a position of a right eye of a user,and light emitted from subpixels in other part of the strip regions topropagate to a position of a left eye of the user. The camera isconfigured to capture an image of the right eye and the left eye of theuser. The controller is configured to determine three-dimensionalpositions of the right eye and the left eye of the user based on theimage captured by the camera, and control an image displayed on thedisplay surface based on the three-dimensional positions of the righteye and the left eye. The optical system is configured to project theimage light emitted from the display surface so as to form a virtualimage in a field of view of the user.

A mobile object according to an embodiment of the present disclosurecomprises a head up display system. The head up display system includesa display surface, an optical element, a camera, a controller, and anoptical system. The display surface includes subpixels arranged in agrid along a horizontal direction and a vertical direction. The opticalelement is configured to: define, for each of strip regions extending ina sertain direction on the display surface, a light ray direction ofimage light emitted from subpixels, wherein an edge of each of the stripregions traverses the subpixels, and a length of a one pixel section ofthe edge along the horizontal direction is shorter than a length of theone pixel section of the edge along the vertical direction; and causelight emitted from subpixels in part of the strip regions to propagateto a position of a right eye of a user, and light emitted from subpixelsin other part of the strip regions to propagate to a position of a lefteye of the user. The camera is configured to capture an image of theright eye and the left eye of the user. The controller is configured todetermine three-dimensional positions of the right eye and the left eyeof the user based on the image captured by the camera, and control animage displayed on the display surface based on the three-dimensionalpositions of the right eye and the left eye. The optical system isconfigured to project the image light emitted from the display surfaceso as to form a virtual image in a field of view of the user.

A three-dimensional display system according to an embodiment of thepresent disclosure comprises a display apparatus having a displaysurface including subpixels arranged in a grid along a horizontaldirection and a vertical direction, and configured to display a left-eyeimage and a right-eye image respectively in first subpixels and secondsubpixels separated by a display boundary on the display surface fromamong the subpixels. The three-dimensional display system comprises abarrier having a light shielding region that shields the left-eye imageand the right-eye image, and a light transmitting region that causes atleast part of the left-eye image to reach a left eye of a user and atleast part of the right-eye image to reach a right eye of the user. Thethree-dimensional display system comprises a detection apparatusconfigured to detect an observation distance from the display apparatusto at least one of the left eye and the right eye. The three-dimensionaldisplay system comprises a controller configured to divide the displaysurface into divided regions arranged in the horizontal direction,depending on the observation distance. The display boundary isperiodically located with a first phase in the horizontal direction in asame divided region, and periodically located with a second phasedifferent from the first phase in the horizontal direction in anadjacent divided region.

A head up display system according to an embodiment of the presentdisclosure comprises a display apparatus having a display surfaceincluding subpixels arranged in a grid along a horizontal direction anda vertical direction, and configured to display a left-eye image and aright-eye image respectively in first subpixels and second subpixelsseparated by a display boundary on the display surface from among thesubpixels. The head up display system comprises a barrier having a lightshielding region that shields the left-eye image and the right-eyeimage, and a light transmitting region that causes at least part of theleft-eye image to reach a left eye of a user and at least part of theright-eye image to reach a right eye of the user. The head up displaysystem comprises a detection apparatus configured to detect anobservation distance from the display apparatus to at least one of theleft eye and the right eye. The head up display system comprises acontroller configured to divide the display surface into divided regionsarranged in the horizontal direction, depending on the observationdistance. The head up display system comprises an optical memberconfigured to cause image light emitted from the display apparatus to beviewed by the user as a virtual image. The display boundary isperiodically located with a first phase in the horizontal direction in asame divided region, and periodically located with a second phasedifferent from the first phase in the horizontal direction in anadjacent divided region.

A mobile object according to an embodiment of the present disclosurecomprises a head up display system. The head up display system includesa display apparatus having a display surface including subpixelsarranged in a grid along a horizontal direction and a verticaldirection, and configured to display a left-eye image and a right-eyeimage respectively in first subpixels and second subpixels separated bya display boundary on the display surface from among the subpixels. Thehead up display system includes a barrier having a light shieldingregion that shields the left-eye image and the right-eye image, and alight transmitting region that causes at least part of the left-eyeimage to reach a left eye of a user and at least part of the right-eyeimage to reach a right eye of the user. The head up display systemincludes a detection apparatus configured to detect an observationdistance from the display apparatus to at least one of the left eye andthe right eye. The head up display system includes a controllerconfigured to divide the display surface into divided regions arrangedin the horizontal direction, depending on the observation distance. Thehead up display system includes an optical member configured to causeimage light emitted from the display apparatus to be viewed by the useras a virtual image. The display boundary is periodically located with afirst phase in the horizontal direction in a same divided region, andperiodically located with a second phase different from the first phasein the horizontal direction in an adjacent divided region.

A three-dimensional display system according to an embodiment of thepresent disclosure comprises a display apparatus having subpixelsarranged in a grid along a first direction and a second directionorthogonal to the first direction, and configured to display a left-eyeimage and a right-eye image respectively in first subpixels and secondsubpixels separated by a display boundary from among the subpixels. Thethree-dimensional display system comprises a barrier having a lightshielding region that shields the left-eye image and the right-eyeimage, and a light transmitting region that causes at least part of theleft-eye image to reach a left eye of a user and at least part of theright-eye image to reach a right eye of the user. The three-dimensionaldisplay system comprises a detection apparatus configured to detectpositions of the left eye and the right eye. The three-dimensionaldisplay system comprises a controller having operation modes betweenwhich orientations of both the left-eye image and the right-eye imagedisplayed by the display apparatus are different. The controller isconfigured to move the display boundary, based on the operation modesand a change in the positions of the left eye and the right eye.

A three-dimensional display system according to an embodiment of thepresent disclosure comprises a display apparatus having subpixelsarranged in a grid along a first direction and a second directionorthogonal to the first direction, and configured to display a left-eyeimage and a right-eye image respectively in first subpixels and secondsubpixels separated by a display boundary from among the subpixels. Thethree-dimensional display system comprises a barrier having a lightshielding region that shields the left-eye image and the right-eyeimage, and a light transmitting region that causes at least part of theleft-eye image to reach a left eye of a user and at least part of theright-eye image to reach a right eye of the user. The three-dimensionaldisplay system comprises a detection apparatus configured to detectpositions of the left eye and the right eye. The three-dimensionaldisplay system comprises a controller configured to move the displayboundary depending on the positions of the left eye and the right eye.The controller is configured to operate in a first mode of causing thedisplay apparatus to display the left-eye image and the right-eye imageso that the first direction of the display apparatus is a lateraldirection as seen from the user, or a second mode of causing the displayapparatus to display the left-eye image and the right-eye image so thatthe second direction of the display apparatus is the lateral directionas seen from the user. The barrier is configured to, between the firstmode and the second mode, maintain a same structure of the lighttransmitting region and the light shielding region, and rotate 90degrees with respect to the display apparatus in a plane along the firstdirection and the second direction.

A three-dimensional display system according to an embodiment of thepresent disclosure comprises a display apparatus having subpixelsarranged in a grid along a first direction and a second directionorthogonal to the first direction, and configured to display a left-eyeimage and a right-eye image respectively in first subpixels and secondsubpixels separated by a display boundary from among the subpixels. Thethree-dimensional display system comprises a barrier having a lightshielding region that shields the left-eye image and the right-eyeimage, and a light transmitting region that causes at least part of theleft-eye image to reach a left eye of a user and at least part of theright-eye image to reach a right eye of the user. The three-dimensionaldisplay system comprises a detection apparatus configured to detectpositions of the left eye and the right eye. The three-dimensionaldisplay system comprises a controller configured to move the displayboundary depending on the positions of the left eye and the right eye.The display apparatus has a pixel formed by subpixels arranged along thefirst direction. The controller is configured to operate in a first modeof causing the display apparatus to display the left-eye image and theright-eye image so that the first direction of the display apparatus isa lateral direction as seen from the user, or a second mode of causingthe display apparatus to display the left-eye image and the right-eyeimage so that the second direction of the display apparatus is thelateral direction as seen from the user. The barrier is configured tomaintain a same barrier inclination angle of the light transmittingregion and the light shielding region between the first mode and thesecond mode, set an opening ratio in the second mode to be lower than anopening ratio in the first mode, and rotate 90 degrees with respect tothe display apparatus in a plane along the first direction and thesecond direction between the first mode and the second mode.

A head up display system according to an embodiment of the presentdisclosure comprises a display apparatus having subpixels arranged in agrid along a first direction and a second direction orthogonal to thefirst direction, and configured to display a left-eye image and aright-eye image respectively in first subpixels and second subpixelsseparated by a display boundary from among the subpixels. The head updisplay system comprises a barrier having a light shielding region thatshields the left-eye image and the right-eye image, and a lighttransmitting region that causes at least part of the left-eye image toreach a left eye of a user and at least part of the right-eye image toreach a right eye of the user. The head up display system comprises adetection apparatus configured to detect positions of the left eye andthe right eye. The head up display system comprises a controller havingoperation modes between which orientations of both the left-eye imageand the right-eye image displayed by the display apparatus aredifferent. The head up display system comprises an optical memberconfigured to cause the left-eye image and the right-eye image to beviewed by the user as a virtual image. The controller is configured tomove the display boundary, based on the operation modes and a change inthe positions of the left eye and the right eye.

A mobile object according to an embodiment of the present disclosurecomprises a head up display system. The head up display system includesa display apparatus having subpixels arranged in a grid along a firstdirection and a second direction orthogonal to the first direction, andconfigured to display a left-eye image and a right-eye imagerespectively in first subpixels and second subpixels separated by adisplay boundary from among the subpixels. The head up display systemincludes a barrier having a light shielding region that shields theleft-eye image and the right-eye image, and a light transmitting regionthat causes at least part of the left-eye image to reach a left eye of auser and at least part of the right-eye image to reach a right eye ofthe user. The head up display system includes a detection apparatusconfigured to detect positions of the left eye and the right eye. Thehead up display system includes a controller having operation modesbetween which orientations of both the left-eye image and the right-eyeimage displayed by the display apparatus are different. The head updisplay system includes an optical member configured to cause theleft-eye image and the right-eye image to be viewed by the user as avirtual image. The controller is configured to move the displayboundary, based on the operation modes and a change in the positions ofthe left eye and the right eye.

Advantageous Effect

It is thus possible to provide a three-dimensional display apparatus, athree-dimensional display system, a head up display, a head up displaysystem, a three-dimensional display apparatus design method, and amobile object having improved techniques of appropriately displaying athree-dimensional image to enhance convenience.

BRIEF DESCRIPTION OF THE DRAWINGS

In the accompanying drawings:

FIG. 1 is a schematic diagram of a three-dimensional display apparatusaccording to an embodiment;

FIG. 2 is a diagram of a display panel in FIG. 1 as seen from the eyesof the user;

FIG. 3 is a diagram illustrating an example of the structure of aparallax barrier;

FIG. 4 is a diagram illustrating pixel arrangement of the display panel;

FIG. 5 is a diagram illustrating a display change of subpixels when thepositions of the eyes of the user change with respect to the displaypanel in FIG. 2;

FIG. 6 is a schematic diagram illustrating the relationships among theinterocular distance, the optimum viewing distance, the gap, the barrierpitch, and the image pitch;

FIG. 7 is a diagram illustrating a comparative example of subpixelarrangement on a display surface;

FIG. 8 is a diagram illustrating a first example of another subpixelarrangement on the display surface;

FIG. 9 is a diagram illustrating a second example of another subpixelarrangement on the display surface;

FIG. 10 is a schematic diagram of a three-dimensional display apparatusin the case where an optical element is a lenticular lens;

FIG. 11 is a schematic diagram of a head up display (HUD) systemaccording to an embodiment;

FIG. 12 is a diagram illustrating an example of a vehicle equipped withthe HUD system illustrated in FIG. 11;

FIG. 13 is a flowchart illustrating a three-dimensional displayapparatus design method;

FIG. 14 is a schematic diagram of a three-dimensional display systemaccording to a first embodiment;

FIG. 15 is a diagram illustrating an example of a HUD equipped with thethree-dimensional display system according to the first embodiment;

FIG. 16 is a diagram illustrating an example of a vehicle equipped withthe HUD illustrated in FIG. 15;

FIG. 17 is a diagram of a display panel and an optical element in FIG.14 as seen from the optical element;

FIG. 18A is a schematic diagram of a display apparatus of athree-dimensional display apparatus according to the first embodiment,illustrating a visible region of a display surface at a referenceposition;

FIG. 18B is a schematic diagram of the display apparatus of thethree-dimensional display apparatus according to the first embodiment,illustrating the visible region of the display surface at a displacementposition;

FIG. 19 is a schematic diagram illustrating the relationships among theinterocular distance, the optimum viewing distance, the gap, the barrierpitch, and the image pitch;

FIG. 20 is a schematic diagram illustrating the relationship between thedisplacement amount of the eye position and the subpixel displaying animage;

FIG. 21A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a conventionalthree-dimensional display apparatus;

FIG. 21B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the conventionalthree-dimensional display apparatus;

FIG. 22A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a three-dimensional displayapparatus according to a second embodiment;

FIG. 22B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the three-dimensionaldisplay apparatus according to the second embodiment;

FIG. 23A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a three-dimensional displayapparatus according to a third embodiment;

FIG. 23B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the three-dimensionaldisplay apparatus according to the third embodiment;

FIG. 24A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a three-dimensional displayapparatus according to a fourth embodiment;

FIG. 24B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the three-dimensionaldisplay apparatus according to the fourth embodiment;

FIG. 25A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a three-dimensional displayapparatus according to a fifth embodiment;

FIG. 25B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the three-dimensionaldisplay apparatus according to the fifth embodiment;

FIG. 26A is a schematic diagram illustrating a visible region of adisplay surface at a reference position in a three-dimensional displayapparatus according to a sixth embodiment;

FIG. 26B is a schematic diagram illustrating the visible region of thedisplay surface at a displacement position in the three-dimensionaldisplay apparatus according to the sixth embodiment;

FIG. 27 is a schematic diagram of a three-dimensional display apparatusin the case where an optical element is a lenticular lens;

FIG. 28 is a functional block diagram illustrating an example of athree-dimensional display system according to an embodiment;

FIG. 29 is a diagram illustrating an example of the structure of athree-dimensional display system according to an embodiment;

FIG. 30 is a diagram illustrating an example of the structure of adisplay apparatus;

FIG. 31 is a diagram illustrating an example of the structure of abarrier;

FIG. 32 is a diagram illustrating an example in which the eyes arelocated at a optimum viewing distance from the barrier;

FIG. 33 is a diagram illustrating an example of a visible region and alight shielding region on the display apparatus;

FIG. 34 is a diagram illustrating an example of a visible region and alight shielding region on the display apparatus;

FIG. 35 is a diagram illustrating an example of the correlation betweenthe HT boundary and the display boundary;

FIG. 36 is a diagram illustrating an example of a dot region and acontrol region in a optimum viewing distance plane;

FIG. 37 is a diagram illustrating an example of a right eye display sameregion in the case where an observation distance is closer than aoptimum viewing distance;

FIG. 38 is a diagram illustrating the width of the right eye displaysame region in the case where the observation distance is shorter thanthe optimum viewing distance;

FIG. 39 is a diagram illustrating an example of a right eye display sameregion in the case where the observation distance is longer than theoptimum viewing distance;

FIG. 40 is a diagram illustrating the width of the right eye displaysame region in the case where the observation distance is longer thanthe optimum viewing distance;

FIG. 41 is a diagram illustrating an example of a right eye display sameboundary determination method in the case where the observation distanceis shorter than the optimum viewing distance;

FIG. 42 is a diagram illustrating an example of a right eye display sameboundary determination method in the case where the observation distanceis longer than the optimum viewing distance;

FIG. 43 is a diagram illustrating an example of equipping athree-dimensional display system according to an embodiment in an HUD;

FIG. 44 is a functional block diagram illustrating an example of athree-dimensional display system according to an embodiment;

FIG. 45 is a diagram illustrating an example of the structure of thethree-dimensional display system according to an embodiment;

FIG. 46 is a diagram illustrating an example of the structure of adisplay apparatus;

FIG. 47 is a diagram illustrating an example of the structure of abarrier;

FIG. 48 is a diagram illustrating an example in which the eyes arelocated at a optimum viewing distance from the barrier;

FIG. 49 is a diagram illustrating an example of a visible region and alight shielding region on the display apparatus;

FIG. 50 is a diagram illustrating an example of a visible region and alight shielding region on the display apparatus;

FIG. 51 is a diagram illustrating an example of the correlation betweenthe head tracking boundary and the display boundary;

FIG. 52 is a diagram illustrating a display example of the displayapparatus in a portrait mode;

FIG. 53 is a diagram illustrating a display example of the displayapparatus in a landscape mode; and

FIG. 54 is a diagram illustrating an example of equipping athree-dimensional display system according to an embodiment in an HUD.

DETAILED DESCRIPTION

Embodiments of the present disclosure will be described below, withreference to the drawings. The drawings referred to in the followingdescription are schematic, and the dimensional ratios and the like inthe drawings do not necessarily correspond to the actual dimensionalratios and the like.

Embodiment 1

A three-dimensional display apparatus has a optimum viewing distance,i.e. a distance optimum for observing a three-dimensional image.Preferably, the optimum viewing distance is allowed to be setappropriately depending on the use environment of the three-dimensionaldisplay apparatus. A three-dimensional display system 1 according to oneof embodiments of the present disclosure has a high degree of freedom insetting the optimum viewing distance.

The three-dimensional display system 1 according to one of embodimentsof the present disclosure includes a detection apparatus 2 and athree-dimensional display apparatus 3, as illustrated in FIG. 1. FIG. 1illustrates the three-dimensional display system 1 as seen from abovethe user.

The detection apparatus 2 detects the position of any of the left andright eyes of the user, and outputs the detected position to acontroller 7. The detection apparatus 2 may include, for example, acamera. The detection apparatus 2 may capture an image of the face ofthe user by the camera. The detection apparatus 2 may detect theposition of at least one of the left and right eyes from the imagecaptured by the camera. The detection apparatus 2 may detect theposition of at least one of the left and right eyes as coordinates in athree-dimensional space, from an image captured by one camera. Thedetection apparatus 2 may detect the position of at least one of theleft and right eyes as coordinates in a three-dimensional space, fromimages captured by two or more cameras.

The detection apparatus 2 may be connected to an external camera,instead of including a camera. The detection apparatus 2 may include aninput terminal to which a signal from the external camera is input. Theexternal camera may be directly connected to the input terminal. Theexternal camera may be indirectly connected to the input terminal via ashared network. The detection apparatus 2 not including a camera mayinclude an input terminal to which a video signal from a camera isinput. The detection apparatus 2 not including a camera may detect theposition of at least one of the left and right eyes from the videosignal input to the input terminal.

The detection apparatus 2 may include, for example, a sensor. The sensormay be an ultrasonic sensor, an optical sensor, or the like. Thedetection apparatus 2 may detect the position of the head of the user bythe sensor, and detect the position of at least one of the left andright eyes based on the position of the head. The detection apparatus 2may detect the position of at least one of the left and right eyes ascoordinates in a three-dimensional space by one or more sensors.

The detection apparatus 2 may detect the moving distance of the left andright eyes along the eyeball arrangement direction, based on thedetection result of the position of at least one of the left and righteyes.

The three-dimensional display system 1 may not include the detectionapparatus 2. In the case where the three-dimensional display system 1does not include the detection apparatus 2, the controller 7 may includean input terminal to which a signal from an external detection apparatusis input. The external detection apparatus may be connected to the inputterminal. The external detection apparatus may use an electrical signaland an optical signal as transmission signals to the input terminal. Theexternal detection apparatus may be indirectly connected to the inputterminal via a shared network. The controller 7 may receive positioncoordinates indicating the position of at least one of the left andright eyes acquired from the external detection apparatus. Thecontroller 7 may calculate the moving distance of the left and righteyes along the horizontal direction, based on the position coordinates.

In the case where the relative positional relationship between a displaypanel 5 of the three-dimensional display apparatus 3 and the eyes of theuser is fixed, the detection apparatus 2 is unnecessary. The controller7 can cause the display panel 5 to display an image based on a preseteye position.

The three-dimensional display apparatus 3 includes an irradiation unit4, the display panel 5 as a display device, a parallax barrier 6 as anoptical element, and the controller 7.

The irradiation unit 4 is located on the side of one surface of thedisplay panel 5, and irradiates the display panel 5 in a planar manner.The irradiation unit 4 may include a light source, a light guide, adiffuser, a diffusion sheet, and the like. The irradiation unit 4 emitsirradiation light by the light source, and homogenizes the irradiationlight in the surface direction of the display panel 5 by the lightguide, the diffuser, the diffusion sheet, or the like. The irradiationunit 4 emits the homogenized light toward the display panel 5.

As the display panel 5, a display panel such as a transmissive liquidcrystal display panel may be used. The display panel 5 has a displaysurface 51 including division regions divided in a first direction (xdirection) and a second direction (y direction) approximately orthogonalto the first direction, as illustrated in FIG. 2. The first direction (xdirection) corresponds to a direction in which the parallax is providedto the eyes of the user. In the three-dimensional display apparatus 3 ofa type in which the user directly views the display panel 5 in a typicalsitting or standing position, the first direction is the horizontaldirection and the second direction is the vertical direction. Hereafter,the first direction is referred to as “x direction”, and the seconddirection is referred to as “y direction”. In the drawings illustratingthe display panel 5, the x direction is indicated as the direction fromright to left, and the y direction is indicated as the direction fromtop to bottom. A direction orthogonal to the x direction and the ydirection and toward the eyes of the user is referred to as “zdirection”.

Each of the division regions corresponds to one subpixel 11. Thesubpixels 11 are arranged in a grid in the x direction and the ydirection. In this embodiment, each subpixel 11 is longer in the xdirection than in the y direction. Each subpixel 11 corresponds to anyof the colors of R (Red), G (Green), and B (Blue). Three subpixels 11 ofR, G, and B as a set can constitute one pixel 12. One pixel 12 can bereferred to as a single pixel. The y direction is, for example, thedirection in which subpixels 11 constituting one pixel 12 are arranged.The arrangement of the subpixels 11 in the y direction is called“column”. The x direction is, for example, the direction in whichsubpixels 11 of the same color are arranged. The arrangement of thesubpixels 11 in the x direction is called “row”.

The display panel 5 is not limited to a transmissive liquid crystalpanel, and may be any other display panel such as an organic EL. In thecase where a light-emitting display panel is used as the display panel5, the irradiation unit 4 is unnecessary.

The parallax barrier 6 defines the light ray direction of image lightemitted from the subpixels 11. For example, the parallax barrier 6includes light shielding regions 61 and light transmitting regions 62arranged in a slit shape extending in a sertain direction, asillustrated in FIG. 3. The parallax barrier 6 determines the visiblerange of image light emitted from the subpixels 11 for each of the leftand right eyes. The parallax barrier 6 may be located on the side of thedisplay panel 5 opposite to the irradiation unit 4, as illustrated inFIG. 1. The parallax barrier 6 may be located on the same side of thedisplay panel 5 as the irradiation unit 4.

The light transmitting regions 62 are parts that transmit light incidenton the parallax barrier 6. The light transmitting regions 62 maytransmit light at transmittance of a first sertain value or more. Forexample, the first sertain value may be 100%, or a value less than 100%.The light shielding regions 61 are parts that shield light incident onthe parallax barrier 6 so as not to pass through. In other words, thelight shielding regions 61 prevent an image displayed on the displaypanel 5 from reaching the eyes of the user. The light shielding region61 may shield light at transmittance of a second sertain value or less.For example, the second sertain value may be 0%, or a value greater thanand close to 0%. The first sertain value may be several times or more,for example, 10 times or more, greater than the second sertain value.

In FIG. 3, the light transmitting regions 62 and the light shieldingregions 61 alternate with each other. The lines indicating the edges ofthe light transmitting regions 62 extend in a direction inclined fromthe y direction by a sertain angle θ. The lines indicating the edges ofthe light transmitting regions 62 can also be regarded as the edges ofthe light transmitting regions 62. The sertain angle θ is also referredto as “barrier inclination angle”. θ may be an angle greater than 0degrees and less than 90 degrees. If the edge of the light transmittingregion 62 extends in the y direction in FIG. 3 and coincides with thearrangement direction of the subpixels 11, moire tends to be recognizedin the display image due to errors contained in the arrangement of thesubpixels 11 and the dimensions of the light transmitting regions 62. Ifthe edge of the light transmitting region 62 extends in the directionhaving the sertain angle with respect to the y direction in FIG. 3,moire is hardly recognized in the display image regardless errorscontained in the arrangement of the subpixels 11 and the dimensions ofthe light transmitting regions 62.

The parallax barrier 6 may be composed of a film or a plate memberhaving transmittance of less than the second sertain value. In thiscase, the light shielding regions 61 are formed by the film or platemember, and the light transmitting regions 62 are formed by openings inthe film or plate member. The film may be made of resin, or made ofother material. The plate member may be made of resin, metal, or thelike, or made of other material. The parallax barrier 6 is not limitedto a film or a plate member, and may be composed of any other type ofmember. The parallax barrier 6 may be composed of a light shieldingsubstrate. The parallax barrier 6 may be composed of a substratecontaining a light shielding additive.

The parallax barrier 6 may be composed of a liquid crystal shutter. Theliquid crystal shutter can control the transmittance of light accordingto an applied voltage. The liquid crystal shutter may be made up ofpixels, and control the transmittance of light in each pixel. The liquidcrystal shutter may form a region with high transmittance of light or aregion with low transmittance of light, in any shape. In the case wherethe parallax barrier 6 is composed of a liquid crystal shutter, thelight transmitting regions 62 may be regions having transmittance of thefirst sertain value or more. In the case where the parallax barrier 6 iscomposed of a liquid crystal shutter, the light shielding regions 61 maybe regions having transmittance of the second sertain value or less.

In FIG. 2, the outline of the parallax barrier 6 as seen from the eyesof the user is indicated on the display surface 51. Image light that haspassed through the light transmitting regions 62 of the parallax barrier6 in FIG. 2 reaches the eyes of the user. Left-eye visible regions 52 onthe display surface 51 as strip regions corresponding to the lighttransmitting regions 62 are visible to the left eye of the user. Imagelight corresponding to the light shielding regions 61 of the parallaxbarrier 6 is shielded before reaching the eyes of the user. The lightshielding regions 61 of the parallax barrier 6 shield part of imagelight. Left-eye light shielding regions 53 on the display surface 51corresponding to the light shielding regions 61 are hardly visible tothe left eye of the user. In FIG. 2, the display surface 51 locatedbehind the light shielding regions 61 of the parallax barrier 6 is shownfor illustrative purposes.

As can be understood from FIG. 1, when an image is viewed from the righteye of the user in the three-dimensional display system 1 of an idealconfiguration, the left-eye light shielding regions 53 on the displaysurface 51 corresponding to the light transmitting regions 62 are atleast partially visible to the user. As a result of image light beingshielded by the light shielding regions 61 of the parallax barrier 6,the left-eye visible regions 52 on the display surface 51 correspondingto the light shielding regions 61 are at least partially not visible tothe right eye of the user. The left-eye light shielding regions 53include right-eye visible regions visible to the right eye. The left-eyelight shielding regions 53 may approximately match the right-eye visibleregions visible to the right eye. The left-eye visible regions 52 areincluded in right-eye light shielding regions not visible to the righteye. The left-eye visible regions 52 may approximately match theright-eye light shielding regions.

By displaying images having parallax in the left-eye visible regions 52visible to the left eye and the right-eye visible regions (included inthe left-eye light shielding regions 53) visible to the right eye, it ispossible to display an image that can be recognized as three-dimensionalto the user's view. Hereafter, an image to be project onto the left eyeis referred to as “left-eye image”, and an image to be project onto theright eye as “right-eye image”. As described above, the parallax barrier6 selectively transmits at least part of the left-eye image displayed inthe left-eye visible regions 52 in the direction of the optical pathtoward the left eye of the user. The parallax barrier 6 also selectivelytransmits at least part of the right-eye image displayed in the left-eyelight shielding regions 53 in the direction of the optical path towardthe right eye of the user.

The controller 7 is connected to each component in the three-dimensionaldisplay system 1, and controls each component. The controller 7 isimplemented, for example, as a processor. The controller 7 may includeone or more processors. The processors may include a general-purposeprocessor that performs a specific function by reading a specificprogram, and a dedicated processor dedicated to a specific process. Thededicated processor may include an application specific integratedcircuit (ASIC). Each processor may include a programmable logic device(PLD). The PLD may include a field-programmable gate array (FPGA). Thecontroller 7 may be any of a system on a chip (SoC) or a system in apackage (SiP) in which one or more processors cooperate with each other.The controller 7 may include memory, and store various information,programs for operating each component in the three-dimensional displaysystem 1, and the like in the memory. The memory may be, for example,semiconductor memory. The memory may function as work memory of thecontroller 7.

The controller 7 determines first subpixels 11L for displaying aleft-eye image and second subpixels 11R for displaying a right-eye imagefrom among the subpixels 11, depending on the positions of the left andright eyes of the user and the structures of the display panel 5 and theparallax barrier 6. The parallax barrier 6 causes the first subpixels11L to be visible to the left eye of the user. The parallax barrier 6causes the second subpixels 11R to be visible to the right eye of theuser. A method of arranging the first subpixels 11L and the secondsubpixels 11R will be described below, with reference to FIG. 2.

FIG. 2 illustrates an example in which the light shielding regions 61and the light transmitting regions 62 of the parallax barrier 6 areequal in width in the x direction. That is, the barrier opening ratio ofthe three-dimensional display apparatus 3 is 50%. In this case, theleft-eye light shielding regions 53 can approximately match theright-eye visible regions. The barrier opening ratio of thethree-dimensional display apparatus 3 is, however, not limited to 50%.To reduce crosstalk, the width of the light shielding regions 61 in thex direction may be greater than the width of the light transmittingregions 62 in the x direction. Crosstalk is a phenomenon whereby part ofa left-eye image is incident on the right eye of the user and/or part ofa right-eye image is incident on the left eye of the user. In the casewhere the width of the light shielding regions 61 in the x direction isgreater than the width of the light transmitting regions 62 in the xdirection, the barrier opening ratio is less than 50%.

In FIG. 2, numbers 1 to 26 are assigned to the subpixels 11 forillustrative purposes. Subpixels 11 of numbers 1 to 13 in FIG. 2 eachhave at least half area belonging to the left-eye visible regions 52,and therefore are set as first subpixels 11L for displaying the left-eyeimage. Subpixels 11 of numbers 14 to 26 in FIG. 2 each have at leasthalf area belonging to the left-eye light shielding regions 53, andtherefore are set as second subpixels 11R for displaying the right-eyeimage. Since the barrier opening ratio is 50% in FIG. 2, the half areais used as a threshold in this example, but the determination method isnot limited to such. In the case where one subpixel 11 has a widerleft-eye visible region 52 than a right-eye visible region, the subpixelcan be regarded as a left-eye visible region 52. In the case where onesubpixel 11 has a wider right-eye visible region than a left-eye visibleregion 52, the subpixel can be regarded as a right-eye visible region.

The first subpixels 11L and the second subpixels 11R can be arrangedaccording to the following rule.

First, a subpixel 11 in the column on the most negative side in the xdirection is assigned number 1. In FIG. 2, the top rightmost subpixel 11is assigned number 1. For example, the subpixel 11 assigned number 1 isa subpixel 11 on the most negative side (the top end in FIG. 2) in the ydirection of the arrangement of successive first subpixels 11L in whichthe left-eye image is to be displayed, at a reference position. Thereference position denotes a state in which the display panel 5, theparallax barrier 6, and the eyes of the user are at a referenceposition. The reference position can correspond to the positionalrelationships among the display panel 5, the parallax barrier 6, and theuser when the eyes of the user view the center of the display panel 5and the parallax barrier 6 from the front.

In the column assigned number 1, numbers 1 to 2r (r is a positiveinteger) are assigned to the respective subpixels 11 in ascending orderin the y direction. Herein, r is a first sertain number. The firstsertain number r can be regarded as the number of subpixels 11 allocatedto one eye. After the number reaches 2r, numbering returns to 1. Thus,numbers 1 to 2r are repeatedly assigned to subpixels 11 in the samecolumn. In the example in FIG. 2, r is 13.

A number obtained by adding t (t is a positive integer less than orequal to r) to the number of each subpixel 11 in the column to which thenumbers have been assigned is assigned to an adjacent subpixel 11 in acolumn adjacent in the x direction (the left in FIG. 2). Herein, t is asecond sertain number. The second sertain number t can be regarded asthe number of subpixels 11 through which the boundary between theleft-eye visible region 52 and the left-eye light shielding region 53passes in the y direction while advancing in the x direction by onepixel. In the case where the number obtained by adding the secondsertain number t is more than 2r, a number obtained by subtracting 2rfrom the number obtained by adding the second sertain number t isassigned to the adjacent subpixel 11. This operation is repeated foradjacent columns in sequence. In the example in FIG. 2, the secondsertain number t is 9.

When the eyes of the user are at the reference position with respect tothe display panel 5 and the parallax barrier 6, of the subpixels 11assigned numbers as described above, subpixels 11 of numbers 1 to r arethe first subpixels 11L for displaying the left-eye image, and subpixels11 of numbers r+1 to 2r are the second subpixels 11R for displaying theright-eye image.

When the length of the subpixel 11 of a pixel in the y direction isdenoted as “vertical pitch Vp” and the length of the subpixel 11 in thex direction is denoted as “horizontal pitch Hp”, the second sertainnumber t and the barrier inclination angle θ satisfy Formula (1-1):

tan θ=Hp/tVp  Formula (1-1).

The horizontal pitch Hp of the subpixel 11 is also referred to as “pixelpitch”.

The arrangement interval of the left-eye visible region 52 and theleft-eye light shielding region 53 in the horizontal direction isreferred to as “image pitch k”. The image pitch k is equal to the widthof the region combining adjacent left-eye visible region 52 and left-eyelight shielding region 53 in the x direction. That is, the image pitch kis the pitch in the x direction with which the left-eye image and theright-eye image are displayed. The image pitch k is the pitch in the xdirection of the light shielding region 61 and the light transmittingregion 62 on the display surface 51 as viewed by the user.

As illustrated in FIG. 4, the first subpixels 11L corresponding tonumbers 1 to 13 and the second subpixels 11R corresponding to numbers 14to 26 are separated by imaginary display boundaries 15 passing along theboundaries between the first subpixels 11L and the second subpixels 11R.The display boundaries 15 are indicated by thick lines in FIG. 4. Thedisplay boundaries 15 have a stepped shape with periodic steps.

The controller 7 can move the display boundaries 15 based on thepositions of the eyes of the user detected by the detection apparatus 2.FIG. 5 illustrates the position of the display boundaries 15 in the casewhere the position of the parallax barrier 6 as seen from the eyes ofthe user is relatively displaced from the position in FIG. 2 to thenegative side (arrow direction) in the x direction. Such movement can bemade in the case where the eyes of the user move relatively to the left.In FIG. 5, the same subpixels 11 as in FIGS. 2 and 4 are given the samenumbers. As illustrated in FIG. 5, when the positions of the eyes of theuser change, the controller 7 displaces the display boundaries 15 toreplace part of the first subpixels 11L and part of the second subpixels11R with each other. For example, in FIG. 5, the first subpixels 11L ofnumbers 11 to 13 for displaying the left-eye image in FIGS. 2 and 4 havechanged to the second subpixels 11R for displaying the right-eye image.Moreover, the second subpixels 11R of numbers 24 to 26 for displayingthe right-eye image in FIGS. 2 and 4 have changed to the first subpixels11L for displaying the left-eye image. The display boundaries 15 as awhole are displaced to the negative side (upward direction in FIG. 5) inthe y direction by 3 times the vertical pitch Vp. The number of firstsubpixels 11L and second subpixels 11R replaced by the controller 7differs depending on the displacement amount of the positions of theeyes of the user.

As illustrated in FIG. 4, the first sertain number r of first subpixels11L and the first sertain number r of second subpixels 11R aresuccessively arranged in each column. Between two adjacent columns, theregions in which the first subpixels 11L and the second subpixels 11Rare arranged are displaced by the second sertain number t of subpixels11 in the y direction. The first sertain number r may be greater thanthe second sertain number t and may not be a multiple of the secondsertain number t. In the case where the first sertain number r is not amultiple of the second sertain number t, the display boundary 15 of thesame shape is periodically repeated in an oblique direction inclinedwith respect to both the y direction and the x direction, as indicatedby the arrows in FIG. 4. In the below-described comparative example inFIG. 7, on the other hand, the display boundary 15 of the same shape isperiodically repeated in the x direction.

The advantage of setting the first sertain number r and the secondsertain number t as described above is a high degree of freedom insetting the optimum viewing distance (optimum viewing distance (OVD)).The optimum viewing distance of the three-dimensional display apparatus3 will be described below, with reference to FIG. 6. The barrier pitchBp, the gap g, the optimum viewing distance d, the user's interoculardistance E, and the image pitch k satisfy the following Formulas (1-2)and (1-3):

E:d=k/2:g  Formula (1-2)

d:Bp=(d+g):k  Formula (1-3),

where the barrier pitch Bp is the pitch of the light transmitting region62 of the parallax barrier 6 in the x direction, and the gap g is thespacing between the display surface 51 and the parallax barrier 6. Thegap g corresponds to a sertain distance. From Formulas (1-2) and (1-3),it is preferable that the image pitch k can be set finely, in order toset the optimum viewing distance d finely.

The capability of the three-dimensional display apparatus 3 and thethree-dimensional display system 1 according to the present disclosureto finely set the image pitch k as compared with a comparative examplewill be described below, with reference to FIGS. 7 to 9.

FIG. 7 is a diagram illustrating an arrangement of the first subpixels11L and the second subpixels 11R on the display surface 51 of athree-dimensional display apparatus according to a comparative example.In FIG. 7, the boundary lines between the left-eye visible regions 52and the left-eye light shielding regions 53 are indicated by straightlines extending in an oblique direction. In the arrangement of thesubpixels 11 in FIG. 7, the first sertain number r=18, and the secondsertain number t=9. Numbers 1 to 18 are assigned to the first subpixels11L, and numbers 19 to 36 are assigned to the second subpixels 11R. Asillustrated in FIG. 7, when the arrangement of the first subpixels 11Land the second subpixels 11R is determined so that r=2t, the value ofthe image pitch k is limited to 4 times the horizontal pitch Hp of thesubpixel 11.

In the case of providing a display panel 5 having subpixels 11, aneasiest structure is to set the image pitch k to an integral multiple ofthe horizontal pitch Hp of the subpixel 11 as illustrated in FIG. 7.With this structure, two first subpixels 11L and two second subpixels11R constantly alternate regularly in the x direction. In athree-dimensional display apparatus having a parallax barrier 6extending in a diagonal direction of subpixels in PTL 1, too, the imagepitch k is an integral multiple of the horizontal pitch Hp. Moreover,displacing the display boundaries 15 in the horizontal direction toprovide parallax in the x direction helps intuitive understanding of theuser.

However, as a result of extensive examination, the inventors discoveredthat the method according to the present disclosure enables arrangementof the first subpixels 11L for the left eye and the second subpixels 11Rfor the right eye without limiting the image pitch k to an integralmultiple of the horizontal pitch Hp. Thus, the image pitch k can be setmore finely than in the case where the image pitch k is set on ahorizontal pitch Hp basis. The image pitch k is determined by thefollowing formula:

k=Hp×2r/t  Formula (1-4).

That is, the image pitch k is approximately equal to a value obtained bymultiplying, by the horizontal pitch Hp which is the pitch of thesubpixel 11 in the first direction, the quotient obtained by dividingtwice the first sertain number r by the second sertain number t. Oncethe image pitch k has been determined, the barrier pitch Bp can bedetermined based on the image pitch k, the optimum viewing distance d,and the gap g. The arrangement of the subpixels 11 in FIG. 2 is based onthis idea. FIGS. 8 and 9 illustrate other examples of arrangement of thesubpixels 11 on the display surface 51 according to an embodiment of thepresent disclosure.

FIG. 8 illustrates arrangement of the subpixels 11 on the displaysurface 51 designed with the first sertain number r=17 and the secondsertain number t=9. The first sertain number r is greater than thesecond sertain number t and is not an integral multiple of the secondsertain number t. With this arrangement of the subpixels 11, the imagepitch k is 34/9 (about 3.78) times the horizontal pitch Hp.

FIG. 9 illustrates arrangement of the subpixels 11 on the displaysurface 51 designed with the first sertain number r=19 and the secondsertain number t=9. The first sertain number r is greater than thesecond sertain number t and is not an integral multiple of the secondsertain number t. With this arrangement of the subpixels 11, the imagepitch k is 38/9 (about 4.22) times the horizontal pitch Hp.

In FIGS. 8 and 9, the image pitch k is a non-integral multiple of thehorizontal pitch Hp. By setting the first sertain number r and thesecond sertain number t as appropriate in this way, the image pitch kcan be set more finely. Thus, the three-dimensional display apparatus 3according to the present disclosure can set the optimum viewing distancewith a higher degree of freedom.

In the foregoing embodiment, the horizontal pitch Hp of the subpixel 11in the x direction which is the parallax direction is longer than thevertical pitch Vp of the subpixel 11. In the case where the subpixels 11are arranged in this way, if the image pitch k is limited to an integralmultiple of the horizontal pitch Hp, the degree of freedom in settingthe optimum viewing distance is particularly low as compared with thecase where the horizontal pitch Hp of the subpixel 11 is shorter thanthe vertical pitch Vp of the subpixel 11, which imposes designconstraints. The three-dimensional display system 1 according to thepresent disclosure can reduce constraints in setting the optimum viewingdistance in the case where the subpixels 11 are longer in the parallaxdirection, and therefore is particularly effective.

FIG. 10 illustrates a three-dimensional display system according to oneof embodiments. In the foregoing embodiment, the three-dimensionaldisplay apparatus 3 includes the parallax barrier 6 as an opticalelement. The three-dimensional display apparatus 3 may include alenticular lens 9 as an optical element, instead of the parallax barrier6. In this case, the lenticular lens 9 may be formed by arrangingcylindrical lenses 10 extending in an oblique direction with respect tothe horizontal direction and the y direction. In the case where thelenticular lens 9 is used as an optical element, the same advantageouseffects as in the case where the parallax barrier 6 is used as anoptical element can be achieved.

In one of embodiments, the three-dimensional display system 1 may beequipped in a head up display 100, as illustrated in FIG. 11. The headup display 100 can be abbreviated as “HUD”. The HUD 100 includes thethree-dimensional display system 1, optical members 110, and aprojection target member 120 having a projection target surface 130. Theoptical members 110 and the projection target member 120 are included inan optical system that projects a virtual image to form in the field ofview of the user. The HUD 100 causes image light emitted from thethree-dimensional display system 1 to reach the projection target member120 via the optical members 110. The HUD 100 causes the image lightreflected off the projection target member 120 to reach the left andright eyes of the user. Thus, the HUD 100 causes the image light totravel from the three-dimensional display system 1 to the left and righteyes of the user along an optical path 140 indicated by dashed lines.The user can view the image light that has reached along the opticalpath 140, as the virtual image 150. The three-dimensional display system1 can provide stereoscopic vision according to the movement of the user,by controlling the display depending on the positions of the left andright eyes of the user.

As illustrated in FIG. 12, the HUD 100, the three-dimensional displaysystem 1, and the three-dimensional display apparatus 3 may be equippedin a mobile object. The HUD 100 and the three-dimensional display system1 have part of their structure shared with another apparatus orcomponent included in the mobile object. For example, the mobile objectmay use a windshield as part of the HUD 100 and the three-dimensionaldisplay system 1. In the case where part of the structure is shared withanother apparatus or component included in the mobile object, the otherstructure can be referred to as “HUD module” or “three-dimensionaldisplay component”.

The term “mobile object” in the present disclosure encompasses vehicles,ships, and aircraft. Vehicles in the present disclosure include motorvehicles and industrial vehicles but are not limited to such, and mayalso include railed vehicles, domestic vehicles, and fixed-wingairplanes running on runways. Motor vehicles include cars, trucks,buses, two-wheeled vehicles, and trolleybuses but are not limited tosuch, and may also include other vehicles that run on roads. Industrialvehicles include industrial vehicles for agriculture and construction.Industrial vehicles include forklifts and golf carts, but are notlimited to such. Industrial vehicles for agriculture include tractors,cultivators, transplanters, binders, combines, and lawn mowers, but arenot limited to such. Industrial vehicles for construction includebulldozers, scrapers, power shovels, crane trucks, dump trucks, and roadrollers, but are not limited to such. Vehicles include human-poweredvehicles. The classifications of vehicles are not limited to theabove-mentioned examples. For example, motor vehicles may includeindustrial vehicles that can run on roads. The same type of vehicle maybelong to classifications. Ships in the present disclosure includepersonal watercraft, boats, and tankers. Aircraft in the presentdisclosure include fixed-wing airplanes and rotary-wing airplanes.

A method of designing the three-dimensional display apparatus 3, thethree-dimensional display system 1, and the HUD 100 (hereafter referredto as “three-dimensional display apparatus, etc.”) according to thepresent disclosure will be described below, with reference to FIG. 13.The method of designing the three-dimensional display apparatus, etc.includes a method of designing the arrangement of the subpixels 11 ofthe display panel 5, the shape of the parallax barrier 6, and the like.

The three-dimensional display apparatus, etc. according to the presentdisclosure are used in various use environments. Accordingly, thespecifications required for the distance from the parallax barrier 6 tothe eyes of the user depend on the use environment to a certain extent.For example, in the case where the HUD is equipped in a vehicle, theposition of the head of the driver as the user is limited to a certainrange. Further, in the case where the HUD is used in a game machine suchas a pachinko machine or a slot machine, the distance from the displayscreen of the game machine to the eyes of the user is limited to acertain extent. Hence, in the design of the three-dimensional displayapparatus, etc. according to the present disclosure, the optimum viewingdistance d depending on the use is determined first (step S01). Theoptimum viewing distance may be determined as a distance having acertain range.

Next, the acceptable range of the image pitch k is determined based onparameters such as the optimum viewing distance d determined in stepS01, the average interocular distance E of the user, and the adoptablerange of the gap g between the display surface 51 and the parallaxbarrier 6 (step S02). Here, with the design method according to thepresent disclosure, the image pitch k need not be limited to an integralmultiple of the horizontal pitch Hp of the display panel 5.

Next, the first sertain number r and the second sertain number t whichare positive integers are determined so that the image pitch k is in therange of the image pitch k determined in step S02 (step S03). Therelationship of the foregoing Formula (1-4) holds between the imagepitch k and the first sertain number r and the second sertain number t.The determined first sertain number r and second sertain number t arestored in and used by the controller 7. When using the three-dimensionaldisplay apparatus, etc., the controller 7 uses the first sertain numberr and the second sertain number t in order to assign the first subpixels11L and the second subpixels 11R to the subpixels 11 on the displaysurface 51 of the display panel 5.

After the first sertain number r and the second sertain number t aredetermined, the barrier inclination angle θ of the parallax barrier 6can be calculated based on the foregoing formula:

tan θ=Hp/tVp  Formula (1-1).

In addition, the barrier pitch Bp of the parallax barrier 6 isdetermined from the image pitch k, the optimum viewing distance d, andthe gap g. The shape of the parallax barrier 6 is thus determined (stepS04).

In this way, the arrangement of the subpixels 11 and the shape of theparallax barrier 6 in the three-dimensional display apparatus, etc. aredetermined. Consequently, the three-dimensional display apparatus, etc.can be formed according to the desired optimum viewing distance.

Embodiment 2

When, in a three-dimensional display system, an opening of a parallaxbarrier is arranged in a diagonal direction of subpixels, crosstalktends to occur depending on the position of the observer's eyes.Crosstalk is a phenomenon that image light for the left eye mixes inimage light for the right eye and reaches the right eye, and image lightfor the right eye mixes in image light for the left eye and reaches theleft eye. If the opening of the parallax barrier is narrowed to preventcrosstalk, the image becomes darker. A three-dimensional display system1001 according to some of embodiments of the present disclosure canreduce crosstalk while suppressing moire and maintaining the openingratio.

Embodiment 2-1

The three-dimensional display system 1001 according to an embodiment ofthe present disclosure includes a detection apparatus 1002 and athree-dimensional display apparatus 1003, as illustrated in FIG. 14. Thethree-dimensional display apparatus 1003 includes an irradiation unit1004, a display panel 1005, a parallax barrier 1006 as an opticalelement, and a controller 1007.

The three-dimensional display system 1001 may be equipped in a head updisplay 1100, as illustrated in FIG. 15. The head up display 1100 can beabbreviated as “HUD”. The HUD 1100 includes the three-dimensionaldisplay system 1001, optical members 1110, and a projection targetmember 1120 having a projection target surface 1130. The HUD 1100 causesimage light emitted from the three-dimensional display system 1001 toreach the projection target member 1120 via the optical members 1110.The HUD 1100 causes the image light reflected off the projection targetmember 1120 to reach the left and right eyes of the user. Thus, the HUD1100 causes the image light to travel from the three-dimensional displaysystem 1001 to the left and right eyes of the user along an optical path1140 indicated by dashed lines. The user can view the image light thathas reached along the optical path 1140, as the virtual image 1150. Thethree-dimensional display system 1001 can provide stereoscopic visionaccording to the movement of the user, by controlling the displaydepending on the positions of the left and right eyes of the user.

As illustrated in FIG. 16, the HUD 1100 and the three-dimensionaldisplay system 1001 may be equipped in a mobile object 1008. The HUD1100 and the three-dimensional display system 1001 have part of theirstructure shared with another apparatus or component included in themobile object. For example, the mobile object 1008 may use a windshieldas part of the HUD 1100 and the three-dimensional display system 1001.In the case where part of the structure is shared with another apparatusor component included in the mobile object, the other structure can bereferred to as “HUD module” or “three-dimensional display component”.The three-dimensional display system 1001 and the three-dimensionaldisplay apparatus 1003 may be equipped in the mobile object.

The detection apparatus 1002 detects the position of any of the left andright eyes of the user, and outputs the detected position to acontroller 1007. The detection apparatus 1002 may include, for example,a camera. The detection apparatus 1002 may capture an image of the faceof the user by the camera. The detection apparatus 1002 may detect theposition of at least one of the left and right eyes from the imagecaptured by the camera. The detection apparatus 1002 may detect theposition of at least one of the left and right eyes as coordinates in athree-dimensional space, from an image captured by one camera. Thedetection apparatus 1002 may detect the position of at least one of theleft and right eyes as coordinates in a three-dimensional space, fromimages captured by two or more cameras.

The detection apparatus 1002 may be connected to an external camera,instead of including a camera. The detection apparatus 1002 may includean input terminal to which a signal from the external camera is input.The external camera may be directly connected to the input terminal. Theexternal camera may be indirectly connected to the input terminal via ashared network. The detection apparatus 1002 not including a camera mayinclude an input terminal to which a video signal from a camera isinput. The detection apparatus 1002 not including a camera may detectthe position of at least one of the left and right eyes from the videosignal input to the input terminal.

The detection apparatus 1002 may include, for example, a sensor. Thesensor may be an ultrasonic sensor, an optical sensor, or the like. Thedetection apparatus 1002 may detect the position of the head of the userby the sensor, and detect the position of at least one of the left andright eyes based on the position of the head. The detection apparatus1002 may detect the position of at least one of the left and right eyesas coordinates in a three-dimensional space by one or more sensors.

The detection apparatus 1002 may detect the moving distance of the leftand right eyes along the eyeball arrangement direction, based on thedetection result of the position of at least one of the left and righteyes.

The three-dimensional display system 1001 may not include the detectionapparatus 1002. In the case where the three-dimensional display system1001 does not include the detection apparatus 1002, the controller 1007may include an input terminal to which a signal from an externaldetection apparatus is input. The external detection apparatus may beconnected to the input terminal. The external detection apparatus mayuse an electrical signal and an optical signal as transmission signalsto the input terminal. The external detection apparatus may beindirectly connected to the input terminal via a shared network. Thecontroller 1007 may receive position coordinates indicating the positionof at least one of the left and right eyes acquired from the externaldetection apparatus. The controller 1007 may calculate the movingdistance of the left and right eyes along the horizontal direction,based on the position coordinates.

An irradiation unit 1004 is located on the side of one surface of thedisplay panel 1005, and irradiates the display panel 1005 in a planarmanner. The irradiation unit 1004 may include a light source, a lightguide, a diffuser, a diffusion sheet, and the like. The irradiation unit1004 emits irradiation light by the light source, and homogenizes theirradiation light in the surface direction of the display panel 1005 bythe light guide, the diffuser, the diffusion sheet, or the like. Theirradiation unit 1004 emits the homogenized light toward the displaypanel 1005.

As the display panel 1005, a display panel such as a transmissive liquidcrystal display panel may be used. The display panel 1005 has, on aplate surface, division regions divided in the horizontal direction andthe vertical direction by a grid-like black matrix 1052, as illustratedin FIG. 17. The division regions can be referred to as “display surface1051”. Each of the division regions corresponds to one subpixel. Theblack matrix 1052 divides the division regions by first black lines 1052a extending in the vertical direction and second black lines 1052 bextending in the horizontal direction. In the black matrix 1052, thefirst black lines 1052 a are arranged in the horizontal direction with aconstant pitch as an example, and the second black lines 1052 b arearranged in the vertical direction with a constant pitch as an example.The subpixels is arranged in a matrix in the horizontal direction andthe vertical direction. Each subpixel corresponds to any of R, G, and B.Three subpixels of R, G, and B as a set can constitute one pixel. Onepixel can be referred to as a single pixel. The horizontal direction is,for example, the direction in which subpixels constituting one pixel arearranged. The vertical direction is, for example, the direction in whichsubpixels of the same color are arranged. The display panel 1005 is notlimited to a transmissive liquid crystal panel, and may be any otherdisplay panel such as an organic EL. In the case where a light-emittingdisplay panel is used as the display panel 1005, the irradiation unit1004 is unnecessary.

The parallax barrier 1006 defines the light ray direction of image lightemitted from the subpixels. The parallax barrier 1006 changes, for eachof open regions 1062 extending in a sertain direction on the displayapparatus, the light ray direction which is the propagation direction ofimage light emitted from the subpixel, as illustrated in FIG. 17. Theparallax barrier 1006 determines the visible range of image lightemitted from the subpixels. The parallax barrier 1006 is located on theside of the display panel 1005 opposite to the irradiation unit 1004, asillustrated in FIG. 14. The parallax barrier 1006 may be located on thesame side of the display panel 1005 as the irradiation unit 1004.

Specifically, the parallax barrier 1006 has light shielding surfaces1061 that shield image light. Two adjacent light shielding surfaces 1061of the light shielding surfaces 1061 define an open region 1062 locatedtherebetween. The open region 1062 has higher light transmittance thanthe light shielding surface 1061. The light shielding surface 1061 haslower light transmittance than the open region 1062.

The open regions 1062 are parts that transmit light incident on theparallax barrier 1006. The open regions 1062 may transmit light attransmittance of a first sertain value or more. For example, the firstsertain value may be 100%, or a value close to 100%. The light shieldingsurfaces 1061 are parts that shield light incident on the parallaxbarrier 1006 so as not to pass through. In other words, the lightshielding surfaces 1061 block an image displayed on the display panel1005. The light shielding surface 1061 may shield light at transmittanceof a second sertain value or less. For example, the second sertain valuemay be 0%, or a value close to 0%.

The open regions 1062 and the light shielding surfaces 1061 alternatewith each other in the horizontal direction and the vertical direction.The edges of the open regions 1062 define, for each of strip regionsextending in a sertain direction on the display surface 1051, the lightray direction of image light emitted from the subpixel. The edge of eachstrip region traverses the subpixels, and the length of a one pixelsection of the edge along the horizontal direction is shorter than thelength of the one pixel section of the edge along the vertical direction

If the line indicating the edge of the open region 1062 extends in thevertical direction, moire tends to be recognized in the display imagedue to errors contained in the arrangement of the subpixels 1011 and thedimensions of the open regions 1062. If the line indicating the edge ofthe open region 1062 extends in a direction having a sertain angle withrespect to the vertical direction, moire is hardly recognized in thedisplay image regardless errors contained in the arrangement of thesubpixels 1011 and the dimensions of the open regions 1062.

The parallax barrier 1006 may be composed of a film or a plate memberhaving transmittance of less than the second sertain value. In thiscase, the light shielding surfaces 1061 are formed by the film or platemember, and the open regions 1062 are formed by openings in the film orplate member. The film may be made of resin, or made of other material.The plate member may be made of resin, metal, or the like, or made ofother material. The parallax barrier 1006 is not limited to a film or aplate member, and may be composed of any other type of member. Theparallax barrier 1006 may have a light shielding substrate. The parallaxbarrier 1006 may have a substrate containing a light shielding additive.

The parallax barrier 1006 may be composed of a liquid crystal shutter.The liquid crystal shutter can control the transmittance of lightaccording to an applied voltage. The liquid crystal shutter may be madeup of pixels, and control the transmittance of light in each pixel. Theliquid crystal shutter may form a region with high transmittance oflight or a region with low transmittance of light, in any shape. In thecase where the parallax barrier 1006 is composed of a liquid crystalshutter, the open regions 1062 may be regions having transmittance ofthe first sertain value or more. In the case where the parallax barrier1006 is composed of a liquid crystal shutter, the light shieldingsurfaces 1061 may be regions having transmittance of the second sertainvalue or less.

The parallax barrier 1006 causes image light emitted from the subpixelsin part of the open regions 1062 to propagate to the position of theright eye of the user, and causes image light emitted from the subpixelsin the other part of the open regions 1062 to propagate to the positionof the left eye of the user. The parallax barrier 1006 is located at asertain distance away from the display surface 1051. The parallaxbarrier 1006 includes the light shielding surfaces 1061 arranged in aslit shape.

Image light that has passed through the open regions 1062 of theparallax barrier 1006 reaches the eyes of the user. Visible regions 1053a as strip regions in FIG. 18A corresponding to the open regions 1062are visible to the left eye of the user. Meanwhile, the light shieldingsurfaces 1061 of the parallax barrier 1006 shield image light beforereaching the eyes of the user. Light shielding regions 1054 acorresponding to the light shielding surfaces 1061 are not visible tothe left eye of the user.

The controller 1007 is connected to each component in thethree-dimensional display system 1001, and controls each component. Thecontroller 1007 is implemented, for example, as a processor. Thecontroller 1007 may include one or more processors. The processors mayinclude a general-purpose processor that performs a specific function byreading a specific program, and a dedicated processor dedicated to aspecific process. The dedicated processor may include an applicationspecific integrated circuit (ASIC). Each processor may include aprogrammable logic device (PLD). The PLD may include afield-programmable gate array (FPGA). The controller 1007 may be any ofa system on a chip (SoC) or a system in a package (SiP) in which one ormore processors cooperate with each other. The controller 1007 mayinclude memory, and store various information, programs for operatingeach component in the three-dimensional display system 1001, and thelike in the memory. The memory may be, for example, semiconductormemory. The memory may function as work memory of the controller 1007.

The controller 1007 determines subpixels for displaying a left-eye imageand subpixels for displaying a right-eye image, depending on thepositions of the eyes of the user and the structures of the displaypanel 1005 and the parallax barrier 1006. To describe a method wherebythe controller 1007 determines the subpixels for displaying each image,the display panel 1005 and the parallax barrier 1006 will be describedin detail below.

As illustrated in FIGS. 18A and 18B, the length in the horizontaldirection of a subpixel P displayed on the display surface 1051 of thedisplay panel 1005 is denoted by Hp, and the length in the verticaldirection of the subpixel P is denoted by Vp. In this case, the absolutevalue of the inclination of a straight line formed by the edge of thevisible region 1053 which is a region on an image that passes throughthe open region 1062 and is visible to the left eye is represented byb×Vp/(a×Hp), using integers a and b (b≥2 and b>a). In the example inFIG. 18A, a=1, and b=2. That is, the inclination of two straight linesdefining the open region 1062 of the display surface 1051 with respectto the horizontal direction is 2×Vp/(1×Hp).

On the display surface 1051, a left-eye image is displayed in a firstsubpixel group Pg1 including (n×b) subpixels P1 to Pm (hereafter, n×b=m)in which n subpixels are successively arranged in the horizontaldirection and b subpixels are successively arranged in the verticaldirection. Herein, m is a value satisfying m≥a+b+1. On the displaysurface 1051, a first subpixel group Pg1 arranged in the same way islocated at a position adjacent to the foregoing first subpixel group Pg1in the vertical direction and shifted by one subpixel in the horizontaldirection, and a left-eye image is displayed therein.

Further, on the display surface 1051, a right-eye image is displayed ina second subpixel group Pgr including m subpixels P(m+1) to P(2×m) thatis adjacent to the first subpixel group Pg1 in the horizontal directionand in which n subpixels are successively arranged in the horizontaldirection as with the first subpixel group Pg1. Thus, n left-eye imagesare successively displayed in the horizontal direction, and n right-eyeimages are successively displayed in the horizontal direction so as tobe adjacent to the left-eye images. The image pitch k which is thearrangement interval of the visible region 1053 in the horizontaldirection is therefore represented by 2n×Hp.

In the example in FIG. 18A, on the display surface 1051, a left-eyeimage is displayed in a first subpixel group Pg1 including six subpixelsP1 to P6 in which three subpixels are successively arranged in thehorizontal direction and two subpixels are successively arranged in thevertical direction. On the display surface 1051, a different left-eyeimage is displayed in a subpixel group Pg1 arranged in the same way andlocated at a position adjacent to the foregoing first subpixel group Pg1in the vertical direction and shifted by one subpixel in the horizontaldirection. Further, on the display surface 1051, a right-eye image isdisplayed in a second subpixel group Pgr including six subpixels P7 toP12 that is adjacent to the first subpixel group Pg1 in the horizontaldirection and in which three subpixels are successively arranged in thehorizontal direction and two subpixels are successively arranged in thevertical direction.

As illustrated in FIG. 19, the barrier pitch Bp which is the arrangementinterval of the open region 1062 of the parallax barrier 1006 and thegap g between the display surface 1051 and the parallax barrier 1006 aredefined so as to satisfy the following Formulas (2-1) and (2-2), where dis the optimum viewing distance and E is the user's interoculardistance:

E:d=(n×Hp):g  Formula (2-1)

d:Bp=(d+g):(2×n×Hp)  Formula (2-2).

The barrier opening width Bw is the width of the open region 1062. Whenm=n×b as mentioned above, the barrier opening width Bw is defineddepending on the optimum viewing distance d and the gap g so that thewidth of the visible region 1053 in the horizontal direction is(m−2)×Hp/b.

In the example in FIG. 18A, the number of each of left-eye images andright-eye images arranged in the horizontal direction is 3, and thenumber of each of left-eye images and right-eye images arranged in thevertical direction is 2. Accordingly, n=3 and b=2, and m=3×2=6. Thebarrier pitch Bp and the barrier opening width Bw are defined so thatthe image pitch k is (2m×Hp)/b=2×6×Hp/2=6×Hp and the width of thevisible region 1053 is (m−2)×Hp/b=(6−2)×Hp/2=2×Hp.

The barrier opening ratio which is the ratio of the width of the visibleregion 1053 to the image pitch k is ((m−2)×Hp/b)/((2n×Hp)/b)=(m−2)/(2m).In the example in FIG. 18A, the barrier opening ratio is(2×Hp/(6×Hp))×100=33%.

The controller 1007 determines subpixels for displaying a left-eye imageand subpixels for displaying a right-eye image, using a displacementfrom a reference position based on the respective position coordinatesof the left and right eyes detected by the detection apparatus 1002. Amethod whereby the controller 1007 determines the subpixels fordisplaying the left-eye image using the displacement from the referenceposition based on the position coordinates of the left eye will bedescribed below. The following description also applies to a methodwhereby the controller 1007 determines the subpixels for displaying theright-eye image using the displacement from the reference position basedon the position coordinates of the right eye.

An image recognized by the left eye of the user in the case where theleft eye of the user is at a displacement position in a displacementdirection from the reference position will be described below. Thedisplacement direction is a direction along a line connecting the leftand right eyes in the case where the user views the display surface 1051in the direction of the normal to the display surface 1051. Thedisplacement position is the position of the eye of the user displacedfrom the reference position.

As described earlier with reference to FIG. 18A, at the referenceposition, the left-eye image is displayed in the subpixels P1 to P6, andthe right-eye image is displayed in the subpixels P7 to P12. A visibleregion 1053 b at the displacement position is different from the visibleregion 1053 a at the reference position, as illustrated in FIG. 18B.Specifically, the part of the subpixel P1 included in the visible region1053 b at the displacement position is smaller than the part of thesubpixel P1 included in the visible region 1053 a at the referenceposition. Moreover, the visible region 1053 b at the displacementposition includes a part of the subpixel P7 not included in the visibleregion 1053 a at the reference position. Consequently, at thedisplacement position, crosstalk caused by mixture of the right-eyeimage and the left-eye image occurs at the left eye of the user.Specifically, the part of the subpixel P7 included in the visible region1053 b is 1/16 of the whole subpixel P7. Since the subpixels included inthe whole visible region 1053 b correspond to four subpixels, thecrosstalk value at the left eye is ( 1/16)/4=1.6%.

In the example in FIG. 18B, the area of the subpixel P1 included in thevisible region 1053 b and the area of the subpixel P7 included in thevisible region 1053 b are equal. In the case where the visible region1053 is more to the right than the visible region 1053 b illustrated inFIG. 18B, the controller 1007 displays the left-eye image in thesubpixel P7 and displays the right-eye image in the subpixel P1. In thecase where the position on the display surface 1051 referenced by theuser through the open region 1062 is more to the left than in the stateillustrated in FIG. 18B, the controller 1007 displays the left-eye imagein the subpixel P1 and displays the right-eye image in the subpixel P7.Thus, the crosstalk value at the left eye does not exceed 1.6% in eithercase. That is, the maximum value of crosstalk is 1.6%.

In other words, the controller 1007 determines the subpixels fordisplaying the left-eye image so that crosstalk does not exceed themaximum value. Specifically, in the case where the visible region 1053is more to the left than in the state illustrated in FIG. 18B, thecontroller 1007 determines the subpixels P1 to P6 for displaying theleft-eye image. In the case where the visible region 1053 is more to theright than in the state illustrated in FIG. 18B, the controller 1007determines the subpixels P2 to P7 for displaying the left-eye image.

The controller 1007 determines the subpixels for displaying the left-eyeimage, based on the displacement amount of the left eye in thedisplacement direction detected by the detection apparatus 1002 and adisplacement threshold. The displacement threshold is E/(n×b), where Eis the interocular distance, i.e. the distance between the eyes of theuser. When the eye of the user moves in the displacement direction byE/(n×b), the left-eye image includes the subpixels right adjacent to thesubpixels included in the left-eye image before the movement by onesubpixel. The displacement amount of the eye of the user is calculatedbased on the position coordinates of the eye of the user. When thedisplacement amount of the left eye is greater than or equal to thethreshold, the controller 1007 determines the subpixels right adjacentby one subpixel, as the subpixels for displaying the left-eye image,

As described above, in each row of the display surface 1051, threesubpixels for displaying the left-eye image are successively arrangedand, adjacent to the three subpixels, three subpixels for displaying theright-eye image are successively arranged. Accordingly, when the lefteye is at a first position Eye1, image light emitted from the subpixelsP2, P4, and P6 in a sertain row of first subpixels passes through theopen region 1062 and reaches the left eye, as illustrated in FIG. 20.The first position Eye1 is a position at which crosstalk is the maximumvalue as illustrated in FIG. 18B.

When the displacement amount detected by the detection apparatus 1002 isE/(3×2) in the right direction (corresponding to a second position Eye 2in FIG. 20), the controller 1007 determines the subpixels P12, P2, andP4 left adjacent to the subpixels P2, P4, and P6 respectively, as thesubpixels for displaying the left-eye image. Likewise, when thedisplacement amount is 2×E/(3×2) in the right direction (correspondingto a third displacement position Eye 3 in FIG. 20), the controller 1007determines the subpixels P10, P12, and P2 left adjacent to the subpixelsP12, P2, and P4 respectively, as the subpixels for displaying theleft-eye image. In the case where subpixels of two rows are controlledtogether as illustrated in, for example, FIGS. 18A and 18B, thecontroller 1007 performs change for each of the 12 subpixels in the tworows. The controller 1007 displays the left-eye image in the subpixelsP1 to P6 at the position Eye1, displays the left-eye image in thesubpixels P12 and P1 to P5 at the position Eye 2, and displays theleft-eye image in the subpixels P11, P12, and P1 to P4 at the positionEye 3.

As described above, in Embodiment 2-1, the edge of the strip region ofthe optical element is configured so that its section crossing over thelength Hp of one pixel of a subpixel in the horizontal direction islonger than its section crossing over the length Vp of one subpixel ofthe subpixel in the vertical direction on the display surface 1051. Thatis, the absolute value of the inclination of the straight line formed bythe edge of the visible region 1053 is greater than 1×Vp/(1×Hp).

According to conventional techniques, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is 1×Vp/(1×Hp). A conventional display surface 1051 having abarrier opening ratio of 33% and designed to prevent crosstalk at areference position as in Embodiment 2-1 includes a first subpixel groupPg1 in which subpixels of one row and three columns for displaying aleft-eye image are arranged and a second subpixel group Pgr in whichsubpixels of one row and three columns for displaying a right-eye imageare arranged, as illustrated in FIG. 21A.

In this case, a visible region 1053 b at a displacement position atwhich crosstalk is maximum as illustrated in FIG. 21B includes a part ofthe subpixel P4 for displaying the right-eye image, so that crosstalkcaused by mixture of the right-eye image and the left-eye image occursat the left eye of the user. Specifically, the part of the subpixel P4included in the visible region 1053 b is ⅛ of the whole subpixel P4.Since the subpixels included in the whole visible region 1053 bcorrespond to two subpixels, the crosstalk value at the left eye is(⅛)/2=6.25%. The crosstalk value in Embodiment 2-1 is 1.6%, as mentionedabove. Thus, crosstalk is reduced as compared with the crosstalk valueof 6.25% of the conventional techniques having the same opening ratio.

Because the absolute value of the inclination of the straight lineformed by the edge of the visible region 1053 is greater than1×Vp/(1×Hp), the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which crosstalk is further reduced. Specifically,while the maximum value of crosstalk in this embodiment is 1.6%, themaximum value of crosstalk is actually less than 1.6% because the partof the subpixel P7, which can cause crosstalk, included in the visibleregion 1053 b is partly the black matrix 1052.

Embodiment 2-2 (in the Case where the Barrier Opening Ratio is 25%)

Embodiment 2-2 of the present disclosure will be described below, withreference to drawings. The schematic diagram of Embodiment 2-2 is thesame as the schematic diagram of Embodiment 2-1, and accordingly itsdescription is omitted. Moreover, the same description as in Embodiment2-1 is omitted.

As illustrated in FIGS. 22A and 22B, in Embodiment 2-2, the firstsubpixel group Pg1 and the second subpixel group Pgr each includesubpixels arranged in two rows and three columns, as in Embodiment 2-1.That is, n=3 and b=2, and m=n×b=3×2=6. In Embodiment 2-1, the barrieropening width Bw is set so that the visible region 1053 a is (m−2)×Hp/bin width. In Embodiment 2-2, the barrier opening width Bw is set so thatthe visible region 1053 a is less than (m−2)×Hp/b in width.Specifically, the barrier pitch Bp and the barrier opening width Bw aredefined so that the image pitch k is 2n×Hp=2×3×Hp=6×Hp and the width ofthe visible region 1053 is less than (m−2)×Hp/b=(6−2)×Hp/2=2×Hp. Here,the barrier opening width Bw is((m+1)−(a+b+1))Hp/b=((6+1)−(1+2+1))Hp/2=1.5 Hp, i.e. a number obtainedby multiplying, by Hp/b, a number obtained by subtracting the value(a+b+1) which is the sum of the maximum number of subpixels that canoverlap with the edge of the visible region 1053 and 1 from the value(m+1) which is the sum of the number of subpixels for one eye and 1, toset the start position of the subpixels for the other eye. Hence, inEmbodiment 2-2, the barrier opening ratio is (1.5×Hp/(6×Hp))×100=25%.

As illustrated in FIG. 22A, at the reference position, the left-eyeimage is displayed in the subpixels P1 to P6, and the right-eye image isdisplayed in the subpixels P7 to P12. A visible region 1053 b at thedisplacement position is different from the visible region 1053 a at thereference position, as illustrated in FIG. 22B. Specifically, the partof the subpixel P1 included in the visible region 1053 a at thereference position is not included in the visible region 1053 b at thedisplacement position. Moreover, the parts of the subpixels P5 and P6included in the visible region 1053 b at the displacement position arelarger than the parts of the subpixels P5 and P6 included in the visibleregion 1053 a at the reference position. Since the left-eye image isdisplayed in all subpixels included in the visible region 1053 b for theleft eye, the crosstalk value is 0%.

In the case where the visible region 1053 b is further shifted to theright as a result of the eye of the user being further displaced fromthe state illustrated in FIG. 22B, a part of the subpixel P7 isincluded, and the subpixel P1 is not included at all. Here, thecontroller 1007 displays the left-eye image in the subpixel P7, anddisplays the right-eye image in the subpixel P1. Thus, the left-eyeimage is displayed in all of the subpixels P2 to P7 referenced by theleft eye, so that the crosstalk value is kept at 0%.

As described above, in Embodiment 2-2, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is greater than 1×Vp/(1×Hp). It is therefore possible toachieve the same advantageous effect as in Embodiment 2-1, i.e.reduction of crosstalk as compared with the crosstalk value of theconventional techniques having the same opening ratio. In addition, inEmbodiment 2-2, the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which the same advantageous effect of reducingcrosstalk as in Embodiment 2-1 can be achieved.

In Embodiment 2-1, the barrier opening width Bw is set so that thevisible region 1053 is less than (m−2)×Hp/b in width. Accordingly, themaximum value of crosstalk can be reduced as compared with Embodiment2-1.

Embodiment 2-3 (in the Case where Each Subpixel Group is Made Up of TwoRows and Two Columns)

Embodiment 2-3 of the present disclosure will be described below, withreference to drawings. The schematic diagram of Embodiment 2-3 is thesame as the schematic diagram of Embodiment 2-1, and accordingly itsdescription is omitted. Moreover, the same description as in Embodiment2-1 is omitted.

In Embodiment 2-1, the first subpixel group Pg1 and the second subpixelgroup Pgr each include subpixels arranged in two rows and three columns.As illustrated in FIGS. 23A and 23B, in Embodiment 2-3, the firstsubpixel group Pg1 and the second subpixel group Pgr each includesubpixels arranged in two rows and two columns. That is, n=2 and b=2,and m=n×b=2×2=4. The barrier pitch Bp and the barrier opening width Bware defined so that the image pitch k is 2n×Hp=2×2×Hp=4×Hp and the widthof the visible region 1053 is (m−2)×Hp/b=(4-2)×Hp/2=1×Hp. Hence, inEmbodiment 2-3, the barrier opening ratio is (1×Hp/(4×Hp))×100=25%.

As illustrated in FIG. 23A, at the reference position, the left-eyeimage is displayed in the subpixels P1 to P4, and the right-eye image isdisplayed in the subpixels P5 to P8. Here, part of each of the subpixelsP1 to P4 is referenced by the left eye, so that the crosstalk value is0%.

When the left eye is displaced, the subpixels included in the visibleregion 1053 b for the left eye change from the visible region 1053 a atthe reference position, as illustrated in FIG. 23B. Specifically, thepart of the subpixel P1 included in the visible region 1053 b at thedisplacement position is smaller than the part of the subpixel P1included in the visible region 1053 a at the reference position.Moreover, the part of the subpixel P5 not included in the visible region1053 a at the reference position is referenced in the visible region1053 b at the displacement position. The right-eye image is displayed inthe subpixel P5. Consequently, at the displacement position, crosstalkcaused by mixture of the left-eye image and the right-eye image occursat the left eye of the user. Specifically, the part of the subpixel P5included in the visible region 1053 b at the displacement position is1/16 of the whole subpixel P5. Since the subpixels included in the wholevisible region 1053 b correspond to two subpixels, the crosstalk valueat the left eye is ( 1/16)/2=3.125%.

In the case where the visible region 1053 b illustrated in FIG. 23B isfurther shifted to the right, the visible region 1053 b includes alarger part of the subpixel P5, and a smaller part of the subpixel P1.Here, the controller 1007 displays the left-eye image in the subpixelP5, and references the right-eye image in the subpixel P1. Thus, thecrosstalk value at the left eye does not exceed 3.125% in either case.

In other words, the controller 1007 determines the subpixels fordisplaying the left-eye image so that crosstalk does not exceed themaximum value. In the example in FIGS. 23A and 23B, in the case wherethe visible region 1053 is more to the left than in the stateillustrated in FIG. 23B, the controller 1007 determines the subpixels P1to P4 for displaying the left-eye image. In the case where the visibleregion 1053 is more to the right than in the state illustrated in FIG.23B, the controller 1007 determines the subpixels P2 to P5 fordisplaying the left-eye image.

As described above, in Embodiment 2-3, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is greater than 1×Vp/(1×Hp). It is therefore possible toachieve the same advantageous effect as in Embodiment 2-1, i.e.reduction of crosstalk as compared with the crosstalk value of theconventional techniques having the same opening ratio. In addition, inEmbodiment 2-3, the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which the same advantageous effect of reducingcrosstalk as in Embodiment 2-1 can be achieved.

Embodiment 2-4 (in the Case where a=1, b=3, and Each Subpixel Group isMade Up of Three Rows and Two Columns)

Embodiment 2-4 of the present disclosure will be described below, withreference to drawings. The schematic diagram of Embodiment 2-4 is thesame as the schematic diagram of Embodiment 2-1, and accordingly itsdescription is omitted. Moreover, the same description as in Embodiment2-1 is omitted.

Embodiment 2-1 describes the case where a=1 and b=2, i.e. theinclination of the barrier inclination angle is 2×Vp/(1×Hp). InEmbodiment 2-4, a=1 and b=3, i.e. the inclination of the barrierinclination angle is 3×Vp/(1×Hp), as illustrated in FIGS. 24A and 24B.Moreover, the first subpixel group Pg1 and the second subpixel group Pgreach include subpixels arranged in three rows and two columns. That is,n=2 and b=3, and m=n×b=2×3=6. The barrier pitch Bp and the barrieropening width Bw are defined so that the image pitch k is 2n×Hp=2×2=4×Hpand the width of the visible region 1053 is 1×Hp which is less than(m−2)×Hp/b=(6−2)×Hp/3=(4/3)×Hp. Hence, in Embodiment 2-4, the barrieropening ratio is (1×Hp/(4×Hp))×100=25%.

As illustrated in FIG. 24A, at the reference position, the left-eyeimage is displayed in the subpixels P1 to P6, and the right-eye image isdisplayed in the subpixels P7 to P12. Here, part of each of thesubpixels P1 to P6 for displaying the left-eye image is included in thevisible region 1053 a for the left eye, so that the crosstalk value is0%.

When the left eye is displaced, the visible region 1053 b for the lefteye is different from the visible region 1053 a for the left eye at thereference position, as illustrated in FIG. 24B. Specifically, the partof the subpixel P1 included in the visible region 1053 b at thedisplacement position is smaller, and the part of the subpixel P7 notincluded in the visible region 1053 a at the reference position isincluded in the visible region 1053 b at the displacement position. Theright-eye image is displayed in the subpixel P7. Consequently, at thedisplacement position, crosstalk caused by mixture of the left-eye imageand the right-eye image occurs at the left eye of the user.Specifically, the part of the subpixel P7 included in the visible region1053 b for the left eye at the displacement position is 1/24 of thewhole subpixel P7. Since the subpixels included in the visible region1053 b for the left eye correspond to three subpixels, the crosstalkvalue at the left eye is ( 1/24)/3=1.39%.

In the case where the visible region 1053 b illustrated in FIG. 24B isfurther shifted to the right, the visible region 1053 b for the left eyeincludes a larger part of the subpixel P7, and a smaller part of thesubpixel P1. Here, the controller 1007 displays the left-eye image inthe subpixel P7, and references the right-eye image in the subpixel P1.Thus, the crosstalk value at the left eye does not exceed 1.39% ineither case.

In other words, the controller 1007 determines the subpixels fordisplaying the left-eye image so that crosstalk does not exceed themaximum value. In the example in FIGS. 24A and 24B, in the case wherethe visible region 1053 is more to the left than in the stateillustrated in FIG. 24B, the controller 1007 determines the subpixels P1to P6 for displaying the left-eye image. In the case where the visibleregion 1053 is more to the right than in the state illustrated in FIG.24B, the controller 1007 determines the subpixels P2 to P7 fordisplaying the left-eye image.

As described above, in Embodiment 2-4, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is greater than 1×Vp/(1×Hp). It is therefore possible toachieve the same advantageous effect as in Embodiment 2-1, i.e.reduction of crosstalk as compared with the crosstalk value of theconventional techniques having the same opening ratio. In addition, inEmbodiment 2-4, the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which the same advantageous effect of reducingcrosstalk as in Embodiment 2-1 can be achieved.

Embodiment 2-5 (in the Case where the Barrier Opening Ratio is 50% andEach Subpixel Group is Made Up of Two Rows and Six Columns)

Embodiment 2-5 of the present disclosure will be described below, withreference to drawings. The schematic diagram of Embodiment 2-5 is thesame as the schematic diagram of Embodiment 2-1, and accordingly itsdescription is omitted. Moreover, the same description as in Embodiment2-1 is omitted.

In Embodiment 2-1, the barrier opening width Bw is set so that thevisible region 1053 is (m−2)×Hp/b in width. In Embodiment 2-5, thebarrier opening width Bw is set so that the visible region 1053 isgreater than (m−2)×Hp/b in width. Specifically, in Embodiment 2-5, thefirst subpixel group Pg1 and the second subpixel group Pgr each includesubpixels arranged in two rows and three columns, as illustrated inFIGS. 25A and 25B. That is, n=3 and b=2, and m=n×b=3×2=6. The barrierpitch Bp and the barrier opening width Bw are defined so that the imagepitch k is 2n×Hp=6×Hp and the width of the visible region 1053 is 3×Hpwhich is greater than (m−2)×Hp/b=(6−2)×Hp/2=2×Hp. Hence, in Embodiment2-5, the barrier opening ratio is (3×Hp/(6×Hp))×100=50%.

In this case, the visibility factor is 50% corresponding to the barrieropening ratio. As illustrated in FIG. 25A, at the reference position,the left-eye image is displayed in the subpixels P1 to P6, and theright-eye image is displayed in the subpixels P7 to P12. Here, thevisible region 1053 a for the left eye includes at least part of each ofthe subpixels P1 to P6 and part of each of the subpixels P12 and P7.Since the right-eye image is displayed in the subpixels P12 and P7,crosstalk occurs at the left eye of the user. The ratio of the part ofthe subpixel P12 included in the visible region 1053 a for the left eyeto the whole subpixel P12 is ¼. Likewise, the ratio of the part of thesubpixel P7 included in the visible region 1053 a to the whole subpixelP7 is ¼. Since the subpixels included in the whole visible region 1053 afor the left eye correspond to six subpixels, the crosstalk value at theleft eye is (¼+¼)/6=8.3%.

When the left eye is displaced, the visible region 1053 b for the lefteye is different from the visible region 1053 a for the left eye at thereference position, as illustrated in FIG. 25B. Specifically, the partsof the subpixels P1 and P12 included in the visible region 1053 b forthe left eye at the displacement position are smaller than the parts ofthe subpixels P1 and P12 included in the visible region 1053 a for theleft eye at the reference position. Moreover, the part of the subpixelP7 included in the visible region 1053 b for the left eye at thedisplacement position is larger. Further, the visible region 1053 b atthe displacement position includes the subpixel P8 not included in thevisible region 1053 a at the reference position. The right-eye image isdisplayed in the subpixels P12, P7, and P8. Consequently, at thedisplacement position, crosstalk caused by mixture of the left-eye imageand the right-eye image occurs at the left eye of the user.Specifically, the crosstalk value at the left eye is 10.4%.

In the case where the visible region 1053 b illustrated in FIG. 25B isfurther shifted to the right, the part of the subpixel P7 referenced bythe left eye is larger, and the part of the subpixel P1 is smaller.Here, the controller 1007 displays the left-eye image in the subpixelP7, and displays the right-eye image in the subpixel P1. Thus, thecrosstalk value at the left eye does not exceed 10.4% in either case.

In other words, the controller 1007 determines the subpixels fordisplaying the left-eye image so that crosstalk does not exceed themaximum value. In the example in FIGS. 25A and 25B, in the case wherethe visible region 1053 is more to the left than in the stateillustrated in FIG. 25B, the controller 1007 determines the subpixels P1to P6 for displaying the left-eye image. In the case where the visibleregion 1053 is more to the right than in the state illustrated in FIG.25B, the controller 1007 determines the subpixels P2 to P7 fordisplaying the left-eye image.

As described above, in Embodiment 2-5, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is greater than 1×Vp/(1×Hp). It is therefore possible toachieve the same advantageous effect as in Embodiment 2-1, i.e.reduction of crosstalk as compared with the crosstalk value of theconventional techniques having the same opening ratio. In addition, inEmbodiment 2-5, the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which the same advantageous effect of reducingcrosstalk as in Embodiment 2-1 can be achieved.

Moreover, in Embodiment 2-5, the visible region 1053 is greater than(m−2)×Hp/b in width. Thus, the barrier opening ratio is higher than thebarrier opening ratio in Embodiment 2-1. The amount of image lightemitted from the display surface 1051 and propagated by the opticalelement 1006 is therefore larger. The user can accordingly recognizemore image light.

Embodiment 2-6 (in the Case where the Barrier Opening Ratio is 50% andEach Subpixel Group is Made Up of Two Rows and Six Columns)

Embodiment 2-6 of the present disclosure will be described below, withreference to drawings. The schematic diagram of Embodiment 2-6 is thesame as the schematic diagram of Embodiment 2-1, and accordingly itsdescription is omitted. Moreover, the same description as in Embodiment2-1 is omitted.

Embodiment 2-6 describes the case where the barrier opening ratio is50%, as in Embodiment 2-5. In Embodiment 2-5, each subpixel groupincludes subpixels arranged in two rows and three columns. In Embodiment2-6, each subpixel group includes subpixels arranged in two rows and sixcolumns. That is, n=6 and b=2, and m=n×b=6×2=12. The barrier pitch Bpand the barrier opening width Bw are defined so that the image pitch kis 2n×Hp=12×Hp and the width of the visible region 1053 is 6×Hp which isgreater than (m−2)×Hp/b=(12−2)×Hp/2=5×Hp. Hence, in Embodiment 2-6, thebarrier opening ratio is (6×Hp/(12×Hp))×100=50%.

As illustrated in FIG. 26A, at the reference position, the left-eyeimage is displayed in the subpixels P1 to P12, and the right-eye imageis displayed in the subpixels P13 to P24. Here, the visible region 1053a for the left eye includes at least part of each of the subpixels P1 toP12 and part of each of the subpixels P24 and P13. Since the left-eyeimage is displayed in the subpixels P1 to P12 and the right-eye image isdisplayed in the subpixels P24 and P13, crosstalk occurs at the left eyeof the user. The ratio of the part of the subpixel P24 included in thevisible region 1053 a for the left eye to the whole subpixel P24 is ¼.Likewise, the ratio of the part of the subpixel P13 included in thevisible region 1053 a to the whole subpixel P13 is ¼. Since thesubpixels included in the whole visible region 1053 correspond to 12subpixels, the crosstalk value at the left eye is (¼+¼)/12=4.2%.

When the left eye is displaced, the visible region 1053 b for the lefteye at the displacement position is different from the visible region1053 a for the left eye at the reference position, as illustrated inFIG. 26B. Specifically, the parts of the subpixels P1 and P2 included inthe visible region 1053 b for the left eye at the displacement positionare smaller than the parts of the subpixels P1 and P2 included in thevisible region 1053 a for the left eye at the reference position.Moreover, the parts of the subpixels P12 and P13 included in the visibleregion 1053 b for the left eye at the displacement position are largerthan the parts of the subpixels P12 and P13 included in the visibleregion 1053 a for the left eye at the reference position. Further, thesubpixel P14 not included in the visible region 1053 a for the left eyeat the reference position is included in the visible region 1053 b atthe displacement position. The right-eye image is displayed in thesubpixels P13 and P14. Consequently, at the displacement position,crosstalk caused by mixture of the left-eye image and the right-eyeimage occurs at the left eye of the user. Specifically, the crosstalkvalue at the left eye is 8.3%.

In the case where the visible region 1053 b illustrated in FIG. 26B isfurther shifted to the right, the controller 1007 displays the left-eyeimage in the subpixel P13, and references the right-eye image in thesubpixel P1. Thus, the crosstalk value at the left eye does not exceed8.3% in either case.

In other words, the controller 1007 determines the subpixels fordisplaying the left-eye image so that crosstalk does not exceed themaximum value. In the example in FIGS. 26A and 26B, in the case wherethe visible region 1053 is more to the left than in the stateillustrated in FIG. 26B, the controller 1007 determines the subpixels P1to P12 for displaying the left-eye image. In the case where the visibleregion 1053 is more to the right than in the state illustrated in FIG.26B, the controller 1007 determines the subpixels P2 to P13 fordisplaying the left-eye image.

As described above, in Embodiment 2-6, the absolute value of theinclination of the straight line formed by the edge of the visibleregion 1053 is greater than 1×Vp/(1×Hp). It is therefore possible toachieve the same advantageous effect as in Embodiment 2-1, i.e.reduction of crosstalk as compared with the crosstalk value of theconventional techniques having the same opening ratio. In addition, inEmbodiment 2-6, the proportion of the black matrix 1052 in a subpixeldisplaying an image that can cause crosstalk at the eye of the user ishigher, as a result of which the same advantageous effect of reducingcrosstalk as in Embodiment 2-1 can be achieved.

Moreover, in Embodiment 2-6, the barrier opening width Bw is set so thatthe visible region 1053 is greater than (m−2)×Hp/b in width. Thus, thebarrier opening ratio is higher than the barrier opening ratio inEmbodiment 2-1. The amount of image light emitted from the displaysurface 1051 and propagated by the optical element 1006 is thereforelarger. The user can accordingly recognize more image light.

Further, in Embodiment 2-6, the image pitch k is higher than the imagepitch k in Embodiment 2-5. Hence, even when a pixel displaying an imagethat can cause crosstalk is included in the visible region 1053 b as aresult of a change in the position of the eye of the user, the crosstalkvalue can be reduced because the total number of pixels included in thevisible region is large.

Although the optical element is the parallax barrier 1006 in theforegoing Embodiments 2-1 to 2-6, the optical element is not limited tosuch. For example, the optical element included in the three-dimensionaldisplay apparatus 1003 may be a lenticular lens 1009. In such a case,the lenticular lens 1009 is formed by arranging, in the horizontaldirection on a plane, cylindrical lenses 1010 extending in the verticaldirection, as illustrated in FIG. 27.

The lenticular lens 1009 causes image light emitted from the subpixelsin part of the visible regions 1053 to propagate to the position of theright eye of the user, and causes image light emitted from the subpixelsin the other part of the visible regions 1053 to propagate to theposition of the left eye of the user, as with the parallax barrier 1006.

Embodiment 3

It is preferable that a three-dimensional display system can keepproviding stereoscopic vision by image processing to a user who changesthe observation distance by moving closer to or farther from thethree-dimensional display system. A three-dimensional display system2001 according to one of embodiments of the present disclosure can keepproviding stereoscopic vision by image processing regardless of a changein the observation distance of the user.

As illustrated in FIGS. 28 and 29, the three-dimensional display system2001 according to an embodiment includes a display apparatus 2010, abarrier 2020, a controller 2030, and a detection apparatus 2040. Thethree-dimensional display system 2001 displays an image by the displayapparatus 2010 and shields part of image light by the barrier 2020, thusallowing different images to be presented to the left eye 2005L of theuser and the right eye 2005R of the user. The user views a binocularparallax image with the left eye 2005L and the right eye 2005R, andtherefore can stereoscopically view the image. The three-dimensionaldisplay system 2001 detects the position of the head of the user by thedetection apparatus 2040, and performs head tracking control ofcontrolling image display depending on the position of the head. Thehead tracking can be abbreviated as “HT”. Hereafter, it is assumed thatthe normal to a display surface 2010 a for displaying an image in thedisplay apparatus 2010 is along the Z-axis direction. It is also assumedthat the user is located in the positive direction of the Z axis withrespect to the display apparatus 2010.

The display apparatus 2010 displays a left-eye image to the left eye2005L of the user, and displays a right-eye image to the right eye 2005Rof the user. The display apparatus 2010 may be, for example, a liquidcrystal device such as a liquid crystal display (LCD). The displayapparatus 2010 may be a self-luminous device such as an organic EL(electro-luminescence) display or an inorganic EL display.

The barrier 2020 is located between the user and the display apparatus2010. The barrier 2020 causes the left-eye image displayed by thedisplay apparatus 2010 to be visible to the left eye 2005L of the userand not visible to the right eye 2005R of the user. The barrier 2020causes the right-eye image displayed by the display apparatus 2010 to bevisible to the right eye 2005R of the user and not visible to the lefteye 2005L of the user. The barrier 2020 may be integrally provided atthe display surface 2010 a of the display apparatus 2010. The barrier2020 may be provided at a sertain distance away from the displayapparatus 2010.

The controller 2030 is connected to each component in thethree-dimensional display system 2001, and controls each component. Thecontroller 2030 is implemented, for example, as a processor. Thecontroller 2030 may include one or more processors. The processors mayinclude a general-purpose processor that performs a specific function byreading a specific program, and a dedicated processor dedicated to aspecific process. The dedicated processor may include an applicationspecific integrated circuit (ASIC). Each processor may include aprogrammable logic device (PLD). The PLD may include afield-programmable gate array (FPGA). The controller 2030 may be any ofa system on a chip (SoC) or a system in a package (SiP) in which one ormore processors cooperate with each other. The controller 2030 mayinclude memory, and store various information, programs for operatingeach component in the three-dimensional display system 2001, and thelike in the memory. The memory may be, for example, semiconductormemory. The memory may function as work memory of the controller 2030.

The detection apparatus 2040 detects the position of any of the left eye2005L and the right eye 2005R of the user, and outputs the detectedposition to the controller 2030. The detection apparatus 2040 mayinclude, for example, a camera. The detection apparatus 2040 may capturean image of the face of the user by the camera. The detection apparatus2040 may detect the position of at least one of the left eye 2005L andthe right eye 2005R from the image captured by the camera. The detectionapparatus 2040 may detect the position of at least one of the left eye2005L and the right eye 2005R as coordinates in a three-dimensionalspace, from an image captured by one camera. The detection apparatus2040 may detect the position of at least one of the left eye 2005L andthe right eye 2005R as coordinates in a three-dimensional space, fromimages captured by two or more cameras.

The detection apparatus 2040 may be connected to an external camera,instead of including a camera. The detection apparatus 2040 may includean input terminal to which a signal from the external camera is input.The external camera may be directly connected to the input terminal. Theexternal camera may be indirectly connected to the input terminal via ashared network. The detection apparatus 2040 not including a camera mayinclude an input terminal to which a video signal from a camera isinput. The detection apparatus 2040 not including a camera may detectthe position of at least one of the left eye 2005L and the right eye2005R from the video signal input to the input terminal.

The detection apparatus 2040 may include, for example, a sensor. Thesensor may be an ultrasonic sensor, an optical sensor, or the like. Thedetection apparatus 2040 may detect the position of the head of the userby the sensor, and detect the position of at least one of the left eye2005L and the right eye 2005R based on the position of the head. Thedetection apparatus 2040 may detect the position of at least one of theleft eye 2005L and the right eye 2005R as coordinates in athree-dimensional space by one or more sensors.

The detection apparatus 2040 detect the distance between at least one ofthe left eye 2005L and the right eye 2005R and the display surface 2010a of the display apparatus 2010 or the barrier 2020, based on thedetection result of the position of at least one of the left eye 2005Land the right eye 2005R. The distance between at least one of the lefteye 2005L and the right eye 2005R and the display surface 2010 a of thedisplay apparatus 2010 or the barrier 2020 is also referred to as“observation distance”. The observation distance is calculated as thedifference between the coordinate in the Z-axis direction of at leastone of the left eye 2005L and the right eye 2005R and the coordinate inthe Z-axis direction of the display surface 2010 a of the displayapparatus 2010 or the barrier 2020.

The three-dimensional display system 2001 may not include the detectionapparatus 2040. In the case where the three-dimensional display system2001 does not include the detection apparatus 2040, the controller 2030may include an input terminal to which a signal from an externaldetection apparatus is input. The external detection apparatus may beconnected to the input terminal. The external detection apparatus mayuse an electrical signal and an optical signal as transmission signalsto the input terminal. The external detection apparatus may beindirectly connected to the input terminal via a shared network. Thecontroller 2030 may calculate, based on the detection result of theposition of at least one of the left eye 2005L and the right eye 2005Racquired from the external detection apparatus, the moving distance ofthe at least one of the left eye 2005L and the right eye 2005R. Thecontroller 2030 may calculate the moving distance of at least one of theleft eye 2005L and the right eye 2005R along the Z-axis direction. Thedetection apparatus 2040 may have the start point and the end point ofdetecting the moving distance, as sertain points. The start point ofdetecting the moving distance may be, for example, the position of atleast one of the left eye 2005L and the right eye 2005R when the imagedisplayed by the display apparatus 2010 is changed as a result of HTcontrol. The end point of detecting the moving distance may be theposition of at least one of the left eye 2005L and the right eye 2005Rwhen the moving distance is detected.

The display apparatus 2010 includes subpixels 2011, as illustrated inFIG. 30 as an example. The subpixels 2011 are arranged in a grid. Thegrid axes representing the arrangement of the subpixels 2011 are assumedto be the X axis and the Y axis. The origin point of the X axis and theY axis may be the center of the display surface 2010 a. Each subpixel2011 has a length in each of the X-axis direction and the Y-axisdirection. The respective lengths of the subpixel 2011 in the X-axisdirection and the Y-axis direction are denoted by Hp and Vp. Hereafter,it is assumed that Vp>Hp. The X-axis direction is also referred to as“horizontal direction” or “first direction”. The Y-axis direction isalso referred to as “vertical direction” or “second direction”.

Subpixels 2011 may constitute a pixel 2012. In FIG. 30, a pixel 2012 iscomposed of three subpixels 2011 enclosed by dashed lines. A pixel 2012may be composed of, for example, subpixels 2011 displaying the colors ofR, G, and B. The number of subpixels 2011 constituting a pixel 2012 isnot limited to three, and may be two, or four or more. In the case wherethe display apparatus 2010 is an LCD or an organic EL display orinorganic EL display, each pixel may correspond to a subpixel 2011 or apixel 2012. In this embodiment, it is assumed that a pixel 2012 iscomposed of subpixels 2011 arranged in the horizontal direction. Inother words, in this embodiment, it is assumed that the horizontaldirection is a direction in which subpixels 2011 constituting a pixel2012 are arranged.

As illustrated in FIG. 30, it is assumed that the display apparatus 2010is used in a state in which the subpixels 2011 constituting the pixel2012 are laterally arranged as seen from the user. In this case, theX-axis direction and the Y-axis direction correspond to the lateraldirection and the longitudinal direction respectively. The ratio of thelongitudinal length and lateral length of the subpixel 2011 as seen fromthe user is also referred to as the “aspect ratio of the subpixel 2011”.In this case, the aspect ratio is Vp/Hp. Hereafter, Vp/Hp is denoted byx (x>1).

The arrangement of the subpixels 2011 is divided by a display boundary2015 in a stepped shape indicated by thick lines. The subpixels 2011included in one arrangement separated by the display boundary 2015 isalso referred to as “first subpixels 2011L”. The subpixels 2011 includedin the other arrangement separated by the display boundary 2015 is alsoreferred to as “second subpixels 2011R”. The display boundary 2015 isnot limited to the shape illustrated in FIG. 30, and may be in othershapes. The display apparatus 2010 displays a left-eye image in thefirst subpixels 2011L, and a right-eye image in the second subpixels2011R. The display boundary 2015 is determined by the controller 2030.The display boundary 2015 may include a first display boundaryindicating a range in which the first subpixels 2011L are arranged, anda second display boundary indicating a range in which the secondsubpixels 2011R are arranged. This makes it possible to expresssubpixels 2011 that are neither the first subpixels 2011L nor the secondsubpixels 2011R.

The barrier 2020 includes light transmitting regions 2021 and lightshielding regions 2022, as illustrated in FIG. 31 as an example. The Xaxis and the Y axis in FIG. 31 correspond to the directions of the Xaxis and the Y axis in FIG. 30.

The light transmitting regions 2021 are parts that transmit lightincident on the barrier 2020. The light transmitting regions 2021 maytransmit light at transmittance of a first sertain value or more. Forexample, the first sertain value may be 100%, or a value close to 100%.The light shielding regions 2022 are parts that shield light incident onthe barrier 2020 so as not to pass through. In other words, the lightshielding regions 2022 shield an image displayed by the displayapparatus 2010. The light shielding region 2022 may shield light attransmittance of a second sertain value or less. For example, the secondsertain value may be 0%, or a value close to 0%.

In FIG. 31, the light transmitting regions 2021 and the light shieldingregions 2022 alternate with each other in the horizontal direction andthe vertical direction. The lines indicating the edges of the lighttransmitting regions 2021 extend in a direction inclined from thevertical direction by a sertain angle θ. The lines indicating the edgesof the light transmitting regions 2021 can also be regarded as the edgesof the light transmitting regions 2021. The sertain angle θ is alsoreferred to as “barrier inclination angle”. θ may be an angle greaterthan 0 degrees and less than 90 degrees. For example, θ may bedetermined to satisfy tan θ=a×Hp/b×Vp (a, b: natural numbers). If theedge of the light transmitting region 2021 extends in the Y-axisdirection in FIG. 31 and coincides with the arrangement direction of thesubpixels 2011, moire tends to be recognized in the display image due toerrors contained in the arrangement of the subpixels 2011 and thedimensions of the light transmitting regions 2021. If the edge of thelight transmitting region 2021 extends in the direction having thesertain angle with respect to the Y-axis direction in FIG. 31, moire ishardly recognized in the display image regardless errors contained inthe arrangement of the subpixels 2011 and the dimensions of the lighttransmitting regions 2021.

The barrier 2020 may be composed of a film or a plate member havingtransmittance of less than the second sertain value. In this case, thelight shielding regions 2022 are formed by the film or plate member, andthe light transmitting regions 2021 are formed by openings in the filmor plate member. The film may be made of resin, or made of othermaterial. The platy member may be made of resin, metal, or the like, ormade of other material. The barrier 2020 is not limited to a film or aplate member, and may be composed of any other type of member. Thebarrier 2020 may be composed of a light shielding substrate. The barrier2020 may be composed of a substrate containing a light shieldingadditive.

The barrier 2020 may be composed of a liquid crystal shutter. The liquidcrystal shutter can control the transmittance of light according to anapplied voltage. The liquid crystal shutter may be made up of pixels,and control the transmittance of light in each pixel. The liquid crystalshutter may form a region with high transmittance of light or a regionwith low transmittance of light, in any shape. In the case where thebarrier 2020 is composed of a liquid crystal shutter, the lighttransmitting regions 2021 may be regions having transmittance of thefirst sertain value or more. In the case where the barrier 2020 iscomposed of a liquid crystal shutter, the light shielding regions 2022may be regions having transmittance of the second sertain value or less.

As illustrated in FIG. 32, it is assumed that the left eye 2005L and theright eye 2005R of the user are located at a optimum viewing distance,denoted by d, from the barrier 2020. The optimum viewing distance isalso referred to as “optical viewing distance (OVD)”. The left eye 2005Land the right eye 2005R can view an image displayed by the displayapparatus 2010 via the barrier 2020. The barrier 2020 includes the lighttransmitting regions 2021 shown as blank and the light shielding regions2022 shown as hatched. The light transmitting regions 2021 and the lightshielding regions 2022 alternate with each other in the X-axisdirection. The pitch with which the light transmitting regions 2021 andthe light shielding regions 2022 alternate is denoted by Bp. Thedistance between the left eye 2005L and the right eye 2005R is alsoreferred to as “interocular distance”, and is donated by E. The distancefrom the barrier 2020 to the display apparatus 2010 is donated by g.

The display apparatus 2010 includes left-eye visible regions 2013L andright-eye visible regions 2013R visible respectively to the left eye2005L and the right eye 2005R of the user via the light transmittingregions 2021. The display apparatus 2010 includes left-eye lightshielding regions 2014L and right-eye light shielding regions 2014R thatare made not visible respectively to the left eye 2005L and the righteye 2005R of the user by the light shielding regions 2022. The linesindicating the edges of the left-eye visible regions 2013L and theright-eye visible regions 2013R correspond to the lines indicating theedges of the light transmitting regions 2021. The lines indicating theedges of the left-eye light shielding regions 2014L and the right-eyelight shielding regions 2014R correspond to the lines indicating theedges of the light shielding regions 2022. The display boundary 2015 maybe located along the line indicating the edge of each of the left-eyevisible region 2013L and the right-eye visible region 2013R. That is,the display boundary 2015 may be located along the edge of the lighttransmitting region 2021.

In the example in FIG. 32, the following assumption is further made. Thelight transmitting region 2021 and the light shielding region 2022 havethe same width, denoted by Bp/2, in the X-axis direction. In theportrait mode, the ratio of the width of the light transmitting region2021 in the X-axis direction to the width of the light transmittingregion 2021 and the light shielding region 2022 in the X-axis directioncan be regarded as an opening ratio. In the example in FIG. 32, theopening ratio of the barrier 2020 is (Bp/2)/Bp, i.e. 50%. In thelandscape mode, the ratio of the width of the light transmitting region2021 in the X-axis direction to the width of the light transmittingregion 2021 and the light shielding region 2022 in the X-axis directioncan be regarded as an opening ratio.

The pitch with which the left-eye visible regions 2013L and theright-eye visible regions 2013R alternate is denoted by k. The left-eyevisible region 2013L and the right-eye visible region 2013R respectivelyhave widths k_(L) and k_(R) in the X-axis direction. In the portraitmode, the left-eye visible region 2013L includes m subpixels successivealong the horizontal direction. In the portrait mode, the right-eyevisible region 2013R includes m successive subpixels. When tanθ=a×Hp/b×Vp, k satisfies a formula k=2 mHp/b. In the landscape mode, theleft-eye visible region 2013L includes j successive subpixels. In theportrait mode, the right-eye visible region 2013R includes j successivesubpixels. When tan θ=(a×Hp)/(b×Vp)=(a×Vp)/(b×x²×Hp), k satisfies aformula k=2×j×Vp/(b×x²). At the OVD, k_(L) and k_(R) are both expressedas k/2. At the OVD, the left-eye visible regions 2013L and the right-eyevisible regions 2013R alternate without a spacing. At the OVD, theleft-eye visible region 2013L and the right-eye light shielding region2014R overlap with each other. At the OVD, the right-eye visible region2013R and the left-eye light shielding region 2014L overlap with eachother.

The relationships among E, k, d, and g illustrated in FIG. 32 aregeometrically determined. The ratio of E and k/2 is equal to the ratioof d and g. In other words, the relationship of Formula (3-1) holds:

E:k/2=d:g  (3-1).

The relationships among Bp, k, d, and g illustrated in FIG. 32 aregeometrically determined. The ratio of Bp and k is equal to the ratio ofd and (d+g). In other words, the relationship of Formula (3-2) holds:

Bp:k=d:(d+g)  (3-2).

In the case where the light transmitting region 2021 and the lightshielding region 2022 have different widths, k_(L) and k_(R) are eachdifferent from k/2. In the case where the light transmitting region 2021is narrower in width than the light shielding region 2022, k_(L) andk_(R) are each less than k/2. In such a case, the left-eye visibleregion 2013L and the right-eye visible region 2013R are arranged with aspacing. As a result of the left-eye visible region 2013L and theright-eye visible region 2013R being arranged with a spacing, crosstalkcaused by a right-eye image reaching the left eye 2005L or a left-eyeimage reaching the right eye 2005R can be reduced. In the case where thelight transmitting region 2021 is greater in width than the lightshielding region 2022, k_(L) and k_(R) are each greater than k/2. Insuch a case, the left-eye visible region 2013L and the right-eye visibleregion 2013R partially overlap with each other. As a result of theleft-eye visible region 2013L and the right-eye visible region 2013Rpartially overlapping with each other, crosstalk occurs. Here, k alsorepresents the pitch of the left-eye visible region 2013L or theright-eye visible region 2013R. Hereafter, the pitch of the left-eyevisible region 2013L or the right-eye visible region 2013R is alsoreferred to as “visible region pitch”.

In the case where the distance between each of the left eye 2005L andthe right eye 2005R and the barrier 2020 is different from the optimumviewing distance, k_(L) and k_(R) are each not limited to k/2. Forexample, in the case where the distance between each of the left eye2005L and the right eye 2005R and the barrier 2020 is longer than theoptimum viewing distance, k_(L) and k_(R) are each less than k/2. Insuch a case, the left-eye visible region 2013L and the right-eye visibleregion 2013R may be arranged with a spacing. For example, in the casewhere the distance between each of the left eye 2005L and the right eye2005R and the barrier 2020 is shorter than the optimum viewing distance,k_(L) and k_(R) are each greater than k/2. In such a case, the left-eyevisible region 2013L and the right-eye visible region 2013R maypartially overlap with each other.

As illustrated in FIG. 33, the display apparatus 2010 as seen from theleft eye 2005L has the left-eye visible region 2013L and the left-eyelight shielding region 2014L. An image displayed in the left-eye visibleregion 2013L is visible to the left eye 2005L. Meanwhile, an imagedisplayed in the left-eye light shielding region 2014L shielded by thelight shielding region 2022 as indicated by hatching is not visible tothe left eye 2005L. In FIG. 33, the left eye 2005L, the left-eye visibleregion 2013L, and the left-eye light shielding region 2014L can bereplaced with the right eye 2005R, the right-eye visible region 2013R,and the right-eye light shielding region 2014R, respectively. Thedisplay apparatus 2010 as seen from the right eye 2005R has theright-eye visible region 2013R and the right-eye light shielding region2014R. An image displayed in the right-eye visible region 2013R isvisible to the right eye 2005R. Meanwhile, an image displayed in theright-eye light shielding region 2014R shielded by the light shieldingregion 2022 as indicated by hatching is not visible to the right eye2005R.

As illustrated in FIG. 34, in the case where the left eye 2005L moves inthe negative direction of the X axis by d_(HT), the left-eye visibleregion 2013L and the left-eye light shielding region 2014L in thedisplay apparatus 2010 move in the positive direction of the X axis byd_(C). In FIG. 34, the left eye 2005L can be replaced with the right eye2005R. In the case where the right eye 2005R moves in the negativedirection of the X axis by d_(HT), the right-eye visible region 2013Rand the right-eye light shielding region 2014R in the display apparatus2010 move in the positive direction of the X axis by d_(C).

As illustrated in FIG. 35, the controller 2030 virtually sets, in asertain plane, head tracking boundaries 2041 arranged in the X-axisdirection based on the shape of the light transmitting region 2021 ofthe barrier 2020. The sertain plane is assumed to be parallel to a planein which the barrier 2020 is located, and away from the barrier 2020 bythe OVD. The head tracking boundaries 2041 are also referred to as “HTboundaries 2041”. The left eye 2005L or the right eye 2005R is locatedin any of head tracking regions 2042 defined by the HT boundaries 2041.The head tracking regions 2042 are also referred to as “HT regions2042”.

The first subpixels 2011L included in the left-eye visible region 2013Lare determined depending on the HT region 2042 in which the left eye2005L is located. For example, in the case where the left eye 2005L islocated in a HT region 2042 a, the left-eye visible region 2013Lindicated by the solid arrow includes subpixels 2011 a, 2011 b, and 2011c. That is, the subpixels 2011 a, 2011 b, and 2011 c are the firstsubpixels 2011L. In the case where the left eye 2005L is located in a HTregion 2042 b, the left-eye visible region 2013L indicated by the dashedarrow includes subpixels 2011 b, 2011 c, and 2011 d. That is, thesubpixels 2011 b, 2011 c, and 2011 d are the first subpixels 2011L.

The interval of the HT boundaries 2041 is expressed as IHT=Hp×d/g, usingHp in FIG. 30, etc. and d and g in FIG. 34, etc. In FIG. 35, the lefteye 2005L can be replaced with the right eye 2005R. The HT boundaries2041 are assumed for each of the left eye 2005L and the right eye 2005R.The HT region 2042 is assumed for each of the left eye 2005L and theright eye 2005R.

In the case where the left-eye visible region 2013L and the right-eyevisible region 2013R move in response to the movement of the left eye2005L and the right eye 2005R, the three-dimensional display system 2001moves the image displayed by the display apparatus 2010 to keepproviding stereoscopic vision to the user. The controller 2030 acquiresthe positions of the left eye 2005L and the right eye 2005R from thedetection apparatus 2040. Based on the positions of the left eye 2005Land the right eye 2005R, the controller 2030 determines the displayboundary 2015 so that the first subpixels 2011L and the second subpixels2011R are respectively located in the left-eye visible region 2013L andthe right-eye visible region 2013R. In other words, when each of theleft eye 2005L and the right eye 2005R passes across the HT boundary2041, the controller 2030 moves the display boundary 2015 in the X-axisdirection by one subpixel.

In the case where the distance d_(C) of the movement of the left-eyevisible region 2013L and the right-eye visible region 2013R in responseto the movement of the left eye 2005L and the right eye 2005R reaches Hpwhich is the length of the subpixel 2011 in the horizontal direction,the controller 2030 may move the left-eye image and the and right-eyeimage displayed by the display apparatus 2010 by one subpixel 2011. Inother words, when the moving distance of the left eye 2005L and theright eye 2005R reaches a control distance indicating the condition formoving the display boundary 2015, the controller 2030 may move thedisplay boundary 2015 by one subpixel 2011. In this case, the controller2030 may acquire, as the moving distance, the distance from the HTboundary 2041 to each of the left eye 2005L and the right eye 2005R. Thecontrol distance is expressed as D_(HT)=(Hp×d)/(g×b), using d and g inFIGS. 32 and 34.

As illustrated in FIG. 36, the display apparatus 2010 includes firstsubpixels 2011L for displaying a left-eye image and second subpixels2011R for displaying a right-eye image. The first subpixels 2011L andthe second subpixels 2011R are separated by the display boundary 2015.Four first subpixels 2011L and four second subpixels 2011R are arrangedin the X-axis direction. The eight subpixels 2011 have respectivenumbers 1 to 8. The number which each subpixel 2011 has is also referredto as the “number of the subpixel 2011”. The first subpixels 2011L havenumbers 5 to 8. The second subpixels 2011R have numbers 1 to 4. Theleft-eye image and the right-eye image are repeatedly displayed in aperiod of eight subpixels 2011.

The number of first subpixels 2011L and the number of second subpixels2011R are the same. The period of the numbers of the subpixels 2011 istwice the number of first subpixels 2011L or second subpixels 2011Rsuccessively arranged. The number of first subpixels 2011L or secondsubpixels 2011R successively arranged may be a sertain number. Thesertain number is not limited to four, and may be three or less, or fiveor more. The left-eye image and the right-eye image may be repeatedlydisplayed in a period of the number of subpixels 2011 twice the sertainnumber.

In FIG. 36, it is assumed that the barrier 2020 is included in thedisplay surface 2010 a of the display apparatus 2010. It is assumed thatthe gap g (see FIGS. 32 and 34) between the display apparatus 2010 andthe barrier 2020 is sufficiently small as compared with the distance dfrom the left eye 2005L and the right eye 2005R to the display surface2010 a of the display apparatus 2010 and is negligible. The followingdescription is based on this assumption.

In FIG. 36, the observation distance is assumed to be equal to dindicating the optimum viewing distance. At the positions of the lefteye 2005L and the right eye 2005R, regions corresponding to the firstsubpixels 2011L and the second subpixels 2011R on the display surface2010 a of the display apparatus 2010 are virtually provided. The regionsvirtually provided at the positions of the left eye 2005L and the righteye 2005R are also referred to as “dot regions 2051”. The dot regions2051 are provided depending on the interocular distance. In FIG. 36, theleft-eye image and the right-eye image are displayed in a period ofeight subpixels 2011. In this case, four dot regions 2051 are allocatedto each of the left eye 2005L and the right eye 2005R. Given that fourdot regions 2051 are located between the left eye 2005L and the righteye 2005R, the width of the dot region 2051 in the X-axis direction iscalculated at ¼ of the interocular distance. The period in which theleft-eye image and the right-eye image are displayed is not limited toeight. The number of dot regions 2051 allocated to each of the left eye2005L and the right eye 2005R is not limited to four. The width of thedot region 2051 in the X-axis direction is calculated by dividing theinterocular distance by the number of dot regions 2051 allocated to eachof the left eye 2005L and the right eye 2005R.

The dot regions 2051 have numbers corresponding to the numbers of thesubpixels 2011. The dot regions 2051 illustrated in FIG. 36 have numbers1 to 8. In the case where the right eye 2005R is located between the dotregions 2051 of numbers 2 and 3, the subpixels 2011 of numbers 1, 2, 3,and 4 are the second subpixels 2011R for displaying the right-eye image.In the case where the left eye 2005L is located between the dot regions2051 of numbers 6 and 7, the subpixels 2011 of numbers 5, 6, 7, and 8are the first subpixels 2011L for displaying the left-eye image. Thus,the dot regions 2051 correspond to the numbers of the subpixels 2011included in the right-eye visible region 2013R and the left-eye visibleregion 2013L. The subpixel 2011 of the number corresponding to thenumber of the dot region 2051 in which the right eye 2005R is located isincluded in the right-eye visible region 2013R. The subpixel 2011 of thenumber corresponding to the number of the dot region 2051 in which theleft eye 2005L is located is included in the left-eye visible region2013L.

At the center of the dot region 2051 in the X-axis direction, a controlboundary 2052 indicated by the “x” mark is set. Each region defined bycontrol boundaries 2052 is referred to as “control region 2053”. Whilethe left eye 2005L is in the same control region 2053, the numbers ofthe subpixels 2011 as the first subpixels 2011L are unchanged. Likewise,while the right eye 2005R is in the same control region 2053, thenumbers of the subpixels 2011 as the second subpixels 2011R areunchanged. In the case where the left eye 2005L moves to a differentcontrol region 2053, the controller 2030 changes the numbers of thesubpixels 2011 as the first subpixels 2011L. Likewise, in the case wherethe right eye 2005R moves to a different control region 2053, thecontroller 2030 changes the numbers of the subpixels 2011 as the secondsubpixels 2011R.

For example, suppose the right eye 2005R moves from the control region2053 including the boundary between the dot regions 2051 of numbers 2and 3 to the control region 2053 including the boundary between the dotregions 2051 of numbers 3 and 4. In this case, the left eye 2005L movesfrom the control region 2053 including the boundary between the dotregions 2051 of numbers 6 and 7 to the control region 2053 including theboundary between the dot regions 2051 of numbers 7 and 8. When the lefteye 2005L and the right eye 2005R each cross over the control boundary2052, the controller 2030 changes the position of the display boundary2015, thus changing the numbers of the subpixels 2011 as the firstsubpixels 2011L and the second subpixels 2011R. After the movement ofthe display boundary 2015, the subpixels 2011 of numbers 2, 3, 4, and 5are the second subpixels 2011R, and the subpixels 2011 of numbers 6, 7,8, and 1 are the first subpixels 2011L.

In FIG. 36, the dot region 2051 and the control region 2053 are eachindicated as a line segment extending in the X-axis direction. The dotregion 2051 and the control region 2053 also extend toward the front andback of the surface of paper. Thus, the dot region 2051 and the controlregion 2053 are planes extending in the X-axis and Y-axis directions. InFIG. 36, the control boundary 2052 is indicated as a midpoint of theline segment representing the dot region 2051 or an end point of theline segment representing the control region 2053. The control boundary2052 also extends toward the front and back of the surface of paper.Thus, the control boundary 2052 is a line having a component in theY-axis direction.

The left eye 2005L and the right eye 2005R can move in a plane that isaway from the display surface 2010 a of the display apparatus 2010 bythe optimum viewing distance and perpendicular to the Z-axis direction.The plane that is away from the display surface 2010 a by the optimumviewing distance and perpendicular to the Z-axis direction is alsoreferred to as “optimum viewing distance plane 2054” (see FIG. 41). Thedot region 2051, the control boundary 2052, and the control region 2053extend in the same direction as the direction in which the edge of thelight transmitting region 2021 of the barrier 2020 extends, in theoptimum viewing distance plane 2054.

In the case where the left eye 2005L is away from the display surface2010 a by the optimum viewing distance, the numbers of the subpixels2011 as the first subpixels 2011L are repeated for all subpixels 2011 ofthe display surface 2010 a. Likewise, in the case where the right eye2005R is away from the display surface 2010 a by the optimum viewingdistance, the numbers of the subpixels 2011 as the second subpixels2011R are repeated for all subpixels 2011 of the display surface 2010 a.

As illustrated in FIG. 37, in the case where the observation distance isshorter than the optimum viewing distance, right-eye image same regions2017 are provided on the display surface 2010 a of the display apparatus2010. The right-eye image same regions 2017 are regions obtained bydividing the display surface 2010 a in the horizontal direction. Inother words, the controller 2030 divides the display surface 2010 a intodivided regions arranged in the horizontal direction. The right-eyeimage same regions 2017 are separated by a right-eye image same boundary2016. The right-eye image same boundary 2016 is a point at which a lineextending from the control boundary 2052 included in each dot region2051 through the right eye 2005R intersects with the display surface2010 a of the display apparatus 2010. For example, the region defined bythe right-eye image same boundaries 2016 specified by the extensionsfrom the control boundaries 2052 respectively included in the dotregions 2051 of numbers 2 and 3 is a right-eye image same region 2017 a.The region defined by the right-eye image same boundaries 2016 specifiedby the extensions from the control boundaries 2052 respectively includedin the dot regions 2051 of numbers 1 and 2 is a right-eye image sameregion 2017 b.

The right eye 2005R in FIG. 37 can be replaced with the left eye 2005L.In the case where the right eye 2005R in FIG. 37 can be replaced withthe left eye 2005L, the right-eye image same boundary 2016 and theright-eye image same region 2017 are respectively replaced with theleft-eye image same boundary and the left-eye image same region. Theright-eye image same region 2017 and the left-eye image same region mayoverlap with each other on the display surface 2010 a. The interval ofthe right-eye image same boundary 2016 or the interval of the left-eyeimage same boundary along the horizontal direction are also referred toas “sertain pitch”.

The right-eye visible region 2013R located in the right-eye image sameregion 2017 a includes the subpixels 2011 of numbers 1, 2, 3, and 4.Accordingly, the controller 2030 sets the subpixels 2011 of numbers 1,2, 3, and 4 as the second subpixels 2011R, in the right-eye image sameregion 2017 a. The right-eye visible region 2013R located in theright-eye image same region 2017 b includes the subpixels 2011 ofnumbers 8, 1, 2, and 3. Accordingly, the controller 2030 sets thesubpixels 2011 of numbers 8, 1, 2, and 3 as the second subpixels 2011R,in the right-eye image same region 2017 b. Thus, the numbers of thesubpixels 2011 as the second subpixels 2011R are different between theright-eye image same regions 2017 a and 2017 b.

In the case where the display surface 2010 a is viewed from the righteye 2005R, the right-eye image same regions 2017 are located on thedisplay surface 2010 a. In the case where the display surface 2010 a isviewed from the left eye 2005L, the left-eye image same regions arelocated on the display surface 2010 a. The left-eye image same regionsare specified depending on the position of the left eye 2005L, as withthe right-eye image same regions 2017. The left-eye image same regionsare divided regions, as with the right-eye image same regions 2017.

The right-eye visible region 2013R and the left-eye visible region 2013Lare located in the right-eye image same regions 2017 a and 2017 b. Theleft-eye visible region 2013L located in the right-eye image sameregions 2017 a and 2017 b is simultaneously located in the left-eyeimage same regions. The numbers of the subpixels 2011 included in theleft-eye visible region 2013L are determined depending on the numbers ofthe dot regions 2051 corresponding to the left-eye image same region.

The numbers of the subpixels 2011 included in the left-eye visibleregion 2013L may overlap with the numbers of the subpixels 2011 includedin the right-eye visible region 2013R. That is, the controller 2030 maybe in a state of simultaneously instructing one subpixel 2011 to displaya left-eye image and display a right-eye image. In a state ofsimultaneously instructing one subpixel 2011 to display a left-eye imageand display a right-eye image, the controller 2030 may set the subpixel2011 preferentially as a first subpixel 2011L, or set the subpixel 2011preferentially as a second subpixel 2011R. In a state of simultaneouslyinstructing one subpixel 2011 to display a left-eye image and display aright-eye image, the controller 2030 may display neither the left-eyeimage nor the right-eye image in the subpixel 2011.

Meanwhile, there may be a subpixel 2011 not included in any of theright-eye visible region 2013R and the left-eye visible region 2013L.The controller 2030 may display an image to be displayed on theassumption that the right eye 2005R and the left eye 2005L are at theoptimum viewing distance, in the subpixel 2011 not included in any ofthe right-eye visible region 2013R and the left-eye visible region2013L. The controller 2030 may display neither the right-eye image northe left-eye image in the subpixel 2011 not included in any of theright-eye visible region 2013R and the left-eye visible region 2013L.

In the right-eye image same region 2017 a, the second display boundaryindicating the position of the second subpixels 2011R is located betweenthe subpixels 2011 of numbers 8 and 1 and between the subpixels 2011 ofnumbers 4 and 5. The second display boundary located between thesubpixels 2011 of numbers 8 and 1 is periodically provided in thehorizontal direction in a period of eight subpixels 2011. The seconddisplay boundary located between the subpixels 2011 of numbers 4 and 5is periodically provided in the horizontal direction in a period ofeight subpixels 2011. The display boundary 2015 including the seconddisplay boundary can be regarded as being provided in a period of twicethe sertain number. The periodic arrangement of the display boundary2015 can be distinguished by a phase indicating the numbers of thesubpixels 2011 between which the display boundary 2015 is located. It isassumed that the phase of the display boundary 2015 located between thesubpixels 2011 of numbers 8 and 1 is number 1. It is equally assumedthat the phase of the display boundary 2015 located between thesubpixels 2011 of numbers 4 and 5 is number 5.

In the right-eye image same region 2017 b, the second display boundaryindicating the position of the second subpixels 2011R is located betweenthe subpixels 2011 of numbers 7 and 8 and between the subpixels 2011 ofnumbers 3 and 4. Hence, in the right-eye image same region 2017 b, thephase of the display boundary 2015 including the second display boundaryis number 8 or 4.

The phase of the display boundary 2015 in the right-eye image sameregion 2017 b is shifted by one subpixel 2011 in the negative directionof the X axis with respect to the phase of the display boundary 2015 inthe right-eye image same region 2017 a. The phase of the displayboundary 2015 in the right-eye image same region 2017 a is also referredto as “first phase”. The phase of the display boundary 2015 in theright-eye image same region 2017 b adjacent to the right-eye image sameregion 2017 a is also referred to as “second phase”. The second phasemay be different from the first phase. The second phase may be shiftedby one subpixel 2011 with respect to the first phase.

The size of the right-eye image same region 2017 in the X-axis directionin the case where the observation distance is shorter than the optimumviewing distance is expressed by the observation distance and theoptimum viewing distance, as illustrated in FIG. 38. The sizes of thedot region 2051 and the right-eye image same region 2017 in the X-axisdirection are respectively denoted by f and s. The observation distanceand the optimum viewing distance are respectively denoted by h and d. Inthis case, the size of the right-eye image same region 2017 in theX-axis direction is expressed by the following Formula (3-3):

s=f×h/(d−h)  (3-3).

As illustrated in FIG. 39, in the case where the observation distance islonger than the optimum viewing distance, too, the right-eye image sameregions 2017 are provided on the display surface 2010 a of the displayapparatus 2010, as in the example in FIG. 37. In FIG. 39, the right-eyeimage same boundary 2016 is a point at which a line extending from theright eye 2005R through the control boundary 2052 included in each dotregion 2051 intersects with the display surface 2010 a of the displayapparatus 2010. For example, the region defined by the right-eye imagesame boundaries 2016 specified by the extensions from the right eye2005R through the control boundaries 2052 respectively included in thedot regions 2051 of numbers 2 and 3 is a right-eye image same region2017 a. The region defined by the right-eye image same boundaries 2016specified by the extensions from the right eye 2005R through the controlboundaries 2052 respectively included in the dot regions 2051 of numbers3 and 4 is a right-eye image same region 2017 c.

In the right-eye image same region 2017 a, the subpixels 2011 of numbers1, 2, 3, and 4 are visible to the right eye 2005R. Accordingly, thecontroller 2030 sets the subpixels 2011 of numbers 1, 2, 3, and 4 as thesecond subpixels 2011R, in the right-eye image same region 2017 a. Inthe right-eye image same region 2017 c, the subpixels 2011 of numbers 2,3, 4, and 5 are visible to the right eye 2005R. Accordingly, thecontroller 2030 sets the subpixels 2011 of numbers 2, 3, 4, and 5 as thesecond subpixels 2011R, in the right-eye image same region 2017 c.

In the right-eye image same region 2017 c, the second display boundaryindicating the position of the second subpixels 2011R is located betweenthe subpixels 2011 of numbers 1 and 2 and between the subpixels 2011 ofnumbers 5 and 6. Hence, in the right-eye image same region 2017 b, thephase of the display boundary 2015 including the second display boundaryis number 2 or 6. The phase of the display boundary 2015 in theright-eye image same region 2017 c is shifted by one subpixel 2011 inthe positive direction of the X axis with respect to the phase of thedisplay boundary 2015 in the right-eye image same region 2017 a. Thephase of the display boundary 2015 in the right-eye image same region2017 c adjacent to the right-eye image same region 2017 a may bereferred to as “second phase”. The direction in which the second phasemoves with respect to the first phase in the case where the observationdistance is shorter than the optimum viewing distance and the directionin which the second phase moves with respect to the first phase in thecase where the observation distance is longer than the optimum viewingdistance are opposite to each other.

The numbers of the second subpixels 2011R in the right-eye image sameregion 2017 b in FIG. 37 are smaller by 1 than the numbers of the secondsubpixels 2011R in the right-eye image same region 2017 a. On the otherhand, the numbers of the second subpixels 2011R in the right-eye imagesame region 2017 c in FIG. 39 are larger by 1 than the numbers of thesecond subpixels 2011R in the right-eye image same region 2017 a. Thatis, the direction of change of the numbers of the second subpixels 2011Rbetween adjacent right-eye image same regions 2017 is different betweenin the case where the observation distance is shorter than the optimumviewing distance and in the case where the observation distance islonger than the optimum viewing distance.

The size of the right-eye image same region 2017 in the X-axis directionin the case where the observation distance is longer than the optimumviewing distance is expressed by the observation distance and theoptimum viewing distance, as illustrated in FIG. 40. The sizes of thedot region 2051 and the right-eye image same region 2017 in the X-axisdirection are respectively denoted by f and s. The observation distanceand the optimum viewing distance are respectively denoted by h and d. Inthis case, the size of the right-eye image same region 2017 in theX-axis direction is expressed by the following Formula (3-4):

s=f×h/(h−d)  (3-4).

In Formula (3-3), (d−h)>0. In Formula (3-4), (h−d)>0. By substituting(d−h) and (h−d) in Formulas (3-3) and (3-4) by lh−dl, the size of theright-eye image same region 2017 in the X-axis direction in each of thecase where the observation distance is shorter than the optimum viewingdistance and the case where the observation distance is longer than theoptimum viewing distance is commonly expressed by the following Formula(3-5):

s=f×h/lh−dl  (3-5).

The three-dimensional display system 2001 according to this embodimentdetermines the display boundary 2015 in each divided region, in the casewhere the observation distance is different from the optimum viewingdistance. Thus, even in the case where the observation distance isdifferent from the optimum viewing distance, the left-eye image and theright-eye image can be displayed so as to respectively reach the lefteye 2005L and the right eye 2005R simply by controlling the imagedisplay, without making the barrier 2020 movable. Consequently, trackingthe movement of the eyes of the user (head tracking) can be performedeasily at low cost. Since stereoscopic vision can be provided regardlessof a change in the observation distance, the range in whichtwo-viewpoint stereoscopic vision can be provided to the user can bewidened.

Suppose a reference point is located in an X-Y plane away from thedisplay surface 2010 a of the display apparatus 2010 by the optimumviewing distance. By virtually providing the reference point, thedistribution of the right-eye image same region 2017 or the left-eyeimage same region on the display surface 2010 a of the display apparatus2010 can be determined easily.

The reference point may be determined depending on an optimal positionfor the user observing the display surface 2010 a of the displayapparatus 2010. The optimal position for the user observing the displaysurface 2010 a of the display apparatus 2010 is also referred to as“optimal observation position”.

The controller 2030 displays a sertain content on the display apparatus2010, to make the user observe the sertain content. The sertain contentmay be, for example, an image in which the right-eye image and theleft-eye image are respectively totally white and totally black. Whenthe user is in a position that is considered as optimal for observingthe sertain content, the controller 2030 acquires the positions of theleft eye 2005L and the right eye 2005R from the detection apparatus2040. The optimal observation position corresponds to the detectedpositions of the left eye 2005L and the right eye 2005R. The optimalobservation position may match the control boundary 2052 in FIG. 36,etc.

The reference point may be determined for each of the left eye 2005L andthe right eye 2005R. In this case, the reference point is the optimalobservation position corresponding to each of the left eye 2005L and theright eye 2005R. The reference point may be one point common to the lefteye 2005L and the right eye 2005R. In this case, for example, thereference point may be a point, such as a midpoint, between the optimalobservation position corresponding to the left eye 2005L and the optimalobservation position corresponding to the right eye 2005R.

In the case where the observation distance is shorter than the optimumviewing distance, the controller 2030 may determine the right-eye imagesame boundary 2016 using a reference point denoted by A in FIG. 41. Thedisplay surface 2010 a of the display apparatus 2010 along the X-Y planeis illustrated in the lower part of FIG. 41. The optimum viewingdistance plane 2054 away from the display surface 2010 a of the displayapparatus 2010 in the positive direction of the Z axis by the optimumviewing distance and parallel to the X-Y plane is illustrated in theupper part of FIG. 41. The optimum viewing distance plane 2054 includesthe dot regions 2051. The optimum viewing distance plane 2054 includesthe control boundaries 2052 that each pass through the dot region 2051and extends in a direction inclined at the barrier inclination anglewith respect to the Y axis. The dot region 2051 extends in a directionalong the control boundary 2052, on the optimum viewing distance plane2054. The right eye 2005R is located between the display surface 2010 aand the optimum viewing distance plane 2054 in the Z-axis direction.

In FIG. 41, the controller 2030 calculates q, as an intersection pointof a dashed line extending from the reference point through the righteye 2005R and the display surface 2010 a. The controller 2030 calculatesq1, as a point away from q in the positive direction of the X-axisdirection by s/2. Here, s is calculated by the foregoing Formula (3-5).The controller 2030 calculates r, as an intersection point of adashed-dotted line extending from q1 in a direction inclined by thebarrier inclination angle with respect to the Y axis and the X axis. Thecontroller 2030 sets a straight line through q1 and r, as the right-eyeimage same boundary 2016. The controller 2030 calculates r1, r2, and r3,as points away from r in the positive and negative directions of the Xaxis by s. The controller 2030 sets lines through r1, r2, and r3 andparallel to a straight line through q1 and r, each as the right-eyeimage same boundary 2016. The right-eye image same boundary 2016 extendsalong the edge of the light transmitting region 2021 of the barrier2020.

In the case where the observation distance is longer than the optimumviewing distance, the controller 2030 may determine the right-eye imagesame boundary 2016 using a reference point denoted by A in FIG. 42. Thedisplay surface 2010 a of the display apparatus 2010 and the optimumviewing distance plane 2054 are illustrated respectively in the lowerand upper parts of FIG. 42, as in FIG. 41. The right eye 2005R islocated on the positive side of the display surface 2010 a and theoptimum viewing distance plane 2054 in the Z-axis direction.

In FIG. 42, the controller 2030 calculates q, as an intersection pointof a dashed line extending from the reference point through the righteye 2005R and the display surface 2010 a. The controller 2030 calculatesq1, as a point away from q in the positive direction of the X-axisdirection by s/2. Here, s is calculated by the foregoing Formula (3-5).The controller 2030 calculates r, as an intersection point of adashed-dotted line extending from q1 in a direction inclined by thebarrier inclination angle with respect to the Y axis and the X axis. Thecontroller 2030 sets a straight line through q1 and r, as the right-eyeimage same boundary 2016. The controller 2030 calculates r1, r2, and r3,as points away from r in the positive and negative directions of the Xaxis by s. The controller 2030 sets lines through r1, r2, and r3 andparallel to a straight line through q1 and r, each as the right-eyeimage same boundary 2016.

The method of determining the right-eye image same boundary 2016corresponding to the right eye 2005R using the reference point has beendescribed above, with reference to FIGS. 41 and 42. As a result ofdetermining the right-eye image same boundary 2016, the right-eye imagesame region 2017 is determined. The controller 2030 determines thenumbers of the subpixels 2011 as the second subpixels 2011R fordisplaying the right-eye image in the range of the right-eye image sameregion 2017. Through the use of the reference point, the numbers of thesubpixels 2011 as the second subpixels 2011R can be determined easilyeven in the case where the observation distance of the user is differentfrom the optimum viewing distance. This eases provision of stereoscopicvision to the user. For the left eye 2005L, too, the left-eye image sameboundary and the left-eye image same region can be determined in thesame way as above. The controller 2030 determines the numbers of thesubpixels 2011 as the first subpixels 2011L for displaying the left-eyeimage in the range of the left-eye image same region.

The three-dimensional display system 2001 according to this embodimentcan keep providing stereoscopic vision to the user by controlling theimage displayed on the display apparatus 2010, even in the case wherethe user moves relative to the display apparatus 2010.

The three-dimensional display system 2001 may be equipped in a head updisplay 2100, as illustrated in FIG. 43. The head up display 2100 can beabbreviated as “HUD 2100”. The HUD 2100 is also referred to as “head updisplay system”. The HUD 2100 includes the three-dimensional displaysystem 2001, an optical member 2110, and a projection target member 2120having a projection target surface 2130. The HUD 2100 causes image lightemitted from the three-dimensional display system 2001 to reach theprojection target member 2120 via the optical member 2110. The HUD 2100causes the image light reflected off the projection target member 2120to reach the left eye 2005L and the right eye 2005R of the user. Thus,the HUD 2100 causes the image light to travel from the three-dimensionaldisplay system 2001 to the left eye 2005L and the right eye 2005R of theuser along an optical path 2140 indicated by dashed lines. The user canview the image light that has reached along the optical path 2140, asthe virtual image 2150. The three-dimensional display system 2001 canprovide stereoscopic vision according to the movement of the user, bycontrolling the display depending on the positions of the left eye 2005Land the right eye 2005R of the user detected by the detection apparatus2040.

The HUD 2100 and the three-dimensional display system 2001 may beequipped in a mobile object. The HUD 2100 and the three-dimensionaldisplay system 2001 have part of their structure shared with anotherapparatus or component included in the mobile object. For example, themobile object may use a windshield as part of the HUD 2100 and thethree-dimensional display system 2001. In the case where part of thestructure is shared with another apparatus or component included in themobile object, the other structure can be referred to as “HUD module” or“three-dimensional display component”. The three-dimensional displaysystem 2001 and the display apparatus 2010 may be equipped in a mobileobject.

The three-dimensional display system 2001 according to the presentdisclosure may provide stereoscopic vision to one user, instead ofproviding stereoscopic vision simultaneously to users.

Embodiment 4

In the case where the left and right eyes of the user are assumed to belaterally aligned, the structure of the barrier of the three-dimensionaldisplay system can be determined depending on the ratio (aspect ratio)of the length of the pixel of the display apparatus in the longitudinaldirection to the length of the pixel in the lateral direction. In thecase where the display apparatus is rotated 90 degrees, the aspect ratioof the pixel is the reciprocal of the aspect ratio in the case where thedisplay apparatus is not rotated. In the case where the aspect ratio isthe reciprocal, the barrier may be required to have a differentstructure for stereoscopic vision. A three-dimensional display system3001 according to one of embodiments of the present disclosure canprovide stereoscopic vision using a barrier of a common structure evenin the case where the aspect ratio of the pixel is the reciprocal.

As illustrated in FIGS. 44 and 45, the three-dimensional display system3001 according to an embodiment includes a display apparatus 3010, abarrier 3020, a controller 3030, and a detection apparatus 3040. Thethree-dimensional display system 3001 displays an image by the displayapparatus 3010 and shields part of image light by the barrier 3020, thusallowing different images to be presented to the left eye 3005L of theuser and the right eye 3005R of the user. The user views a binocularparallax image with the left eye 3005L and the right eye 3005R, andtherefore can stereoscopically view the image. The three-dimensionaldisplay system 3001 detects the position of the head of the user by thedetection apparatus 3040, and performs head tracking control ofcontrolling image display depending on the position of the head. Thehead tracking can be abbreviated as “HT”. Hereafter, it is assumed thatthe normal to a display surface 3010 a for displaying an image in thedisplay apparatus 3010 is along the Z-axis direction. It is also assumedthat the user is located in the positive direction of the Z axis withrespect to the display apparatus 3010.

The display apparatus 3010 displays a left-eye image to the left eye3005L of the user, and displays a right-eye image to the right eye 3005Rof the user. The display apparatus 3010 may be, for example, a liquidcrystal device such as a liquid crystal display (LCD). The displayapparatus 3010 may be a self-luminous device such as an organic EL(electro-luminescence) display or an inorganic EL display.

The barrier 3020 is located between the user and the display apparatus3010. The barrier 3020 causes the left-eye image displayed by thedisplay apparatus 3010 to be visible to the left eye 3005L of the userand not visible to the right eye 3005R of the user. The barrier 3020causes the right-eye image displayed by the display apparatus 3010 to bevisible to the right eye 3005R of the user and not visible to the lefteye 3005L of the user. The barrier 3020 may be integrally provided atthe display surface 3010 a of the display apparatus 3010. The barrier3020 may be provided at a sertain distance away from the displayapparatus 3010.

The controller 3030 is connected to each component in thethree-dimensional display system 3001, and controls each component. Thecontroller 3030 is implemented, for example, as a processor. Thecontroller 3030 may include one or more processors. The processors mayinclude a general-purpose processor that performs a specific function byreading a specific program, and a dedicated processor dedicated to aspecific process. The dedicated processor may include an applicationspecific integrated circuit (ASIC). Each processor may include aprogrammable logic device (PLD). The PLD may include afield-programmable gate array (FPGA). The controller 3030 may be any ofa system on a chip (SoC) or a system in a package (SiP) in which one ormore processors cooperate with each other. The controller 3030 mayinclude memory, and store various information, programs for operatingeach component in the three-dimensional display system 3001, and thelike in the memory. The memory may be, for example, semiconductormemory. The memory may function as work memory of the controller 3030.

The detection apparatus 3040 detects the position of any of the left eye3005L and the right eye 3005R of the user, and outputs the detectedposition to the controller 3030. The detection apparatus 3040 mayinclude, for example, a camera. The detection apparatus 3040 may capturean image of the face of the user by the camera. The detection apparatus3040 may detect the position of at least one of the left eye 3005L andthe right eye 3005R from the image captured by the camera. The detectionapparatus 3040 may detect the position of at least one of the left eye3005L and the right eye 3005R as coordinates in a three-dimensionalspace, from an image captured by one camera. The detection apparatus3040 may detect the position of at least one of the left eye 3005L andthe right eye 3005R as coordinates in a three-dimensional space, fromimages captured by two or more cameras.

The detection apparatus 3040 may be connected to an external camera,instead of including a camera. The detection apparatus 3040 may includean input terminal to which a signal from the external camera is input.The external camera may be directly connected to the input terminal. Theexternal camera may be indirectly connected to the input terminal via ashared network. The detection apparatus 3040 not including a camera mayinclude an input terminal to which a video signal from a camera isinput. The detection apparatus 3040 not including a camera may detectthe position of at least one of the left eye 3005L and the right eye3005R from the video signal input to the input terminal.

The detection apparatus 3040 may include, for example, a sensor. Thesensor may be an ultrasonic sensor, an optical sensor, or the like. Thedetection apparatus 3040 may detect the position of the head of the userby the sensor, and detect the position of at least one of the left eye3005L and the right eye 3005R based on the position of the head. Thedetection apparatus 3040 may detect the position of at least one of theleft eye 3005L and the right eye 3005R as coordinates in athree-dimensional space by one or more sensors.

The detection apparatus 3040 may detect the moving distance of at leastone of the left eye 3005L and the right eye 3005R along the X-axisdirection or the Y-axis direction, based on the detection result of theposition of at least one of the left eye 3005L and the right eye 3005R.The detection apparatus 3040 may detect the moving distance of at leastone of the left eye 3005L and the right eye 3005R along the Z-axisdirection. The detection apparatus 3040 may have the start point and theend point of detecting the moving distance, as sertain points. The startpoint of detecting the moving distance may be, for example, the positionof at least one of the left eye 3005L and the right eye 3005R when theimage displayed by the display apparatus 3010 is changed as a result ofHT control. The end point of detecting the moving distance may be theposition of at least one of the left eye 3005L and the right eye 3005Rwhen the moving distance is detected.

The three-dimensional display system 3001 may not include the detectionapparatus 3040. In the case where the three-dimensional display system3001 does not include the detection apparatus 3040, the controller 3030may include an input terminal to which a signal from an externaldetection apparatus is input. The external detection apparatus may beconnected to the input terminal. The external detection apparatus mayuse an electrical signal and an optical signal as transmission signalsto the input terminal. The external detection apparatus may beindirectly connected to the input terminal via a shared network. Thecontroller 3030 may calculate, based on the detection result of theposition of at least one of the left eye 3005L and the right eye 3005Racquired from the external detection apparatus, the moving distance ofthe at least one of the left eye 3005L and the right eye 3005R. Thecontroller 3030 may calculate the moving distance of the left eye 3005Land the right eye 3005R along the Z-axis direction.

The display apparatus 3010 includes subpixels 3011, as illustrated inFIG. 46 as an example. The subpixels 3011 are arranged in a grid. Thegrid axes representing the arrangement of the subpixels 3011 are assumedto be the X axis and the Y axis. The origin point of the X axis and theY axis may be the center of the display surface 3010 a. Each subpixel3011 has a length in each of the X-axis direction and the Y-axisdirection. The respective lengths of the subpixel 3011 in the X-axisdirection and the Y-axis direction are denoted by Hp and Vp. Hereafter,it is assumed that Vp>Hp. The X-axis direction is also referred to as“horizontal direction” or “first direction”. The Y-axis direction isalso referred to as “vertical direction” or “second direction”.

Subpixels 3011 may constitute a pixel 3012. In FIG. 46, a pixel 3012 iscomposed of three subpixels 3011 enclosed by dashed lines. A pixel 3012may be composed of, for example, subpixels 3011 displaying the colors ofR, G, and B. The number of subpixels 3011 constituting a pixel 3012 isnot limited to three, and may be two, or four or more. In the case wherethe display apparatus 3010 is an LCD or an organic EL display orinorganic EL display, each pixel may correspond to a subpixel 3011 or apixel 3012. In this embodiment, it is assumed that a pixel 3012 iscomposed of subpixels 3011 arranged in the horizontal direction. Inother words, in this embodiment, it is assumed that the horizontaldirection is a direction in which subpixels 3011 constituting a pixel3012 are arranged.

As illustrated in FIG. 46, in the case where the subpixels 3011constituting the pixel 3012 are laterally arranged as seen from theuser, the X-axis direction and the Y-axis direction correspond to thelateral direction and the longitudinal direction respectively. The ratioof the longitudinal length to the lateral length of the subpixel 3011 asseen from the user is also referred to as the “aspect ratio of thesubpixel 3011”. In this case, the aspect ratio is Vp/Hp. Hereafter,Vp/Hp is denoted by x (x>1). In the case where the display apparatus3010 illustrated in FIG. 46 rotates 90 degrees, the subpixels 3011constituting the pixel 3012 are longitudinally arranged as seen from theuser. In the case where the subpixels 3011 are longitudinally arrangedas seen from the user, the X-axis direction and the Y-axis directioncorrespond to the longitudinal direction and the lateral directionrespectively. In this case, the aspect ratio of the subpixel 3011 isHp/Vp. Hp/Vp is denoted by 1/x. Thus, as a result of the displayapparatus 3010 rotating 90 degrees relative to the user, the aspectratio of the subpixel 3011 becomes the reciprocal.

The arrangement of the subpixels 3011 is divided by a display boundary3015 in a stepped shape indicated by thick lines. The subpixels 3011included in one arrangement separated by the display boundary 3015 isalso referred to as “first subpixels 3011L”. The subpixels 3011 includedin the other arrangement separated by the display boundary 3015 is alsoreferred to as “second subpixels 3011R”. The display boundary 3015 isnot limited to the shape illustrated in FIG. 46, and may be in othershapes. The display apparatus 3010 displays a left-eye image in thefirst subpixels 3011L, and a right-eye image in the second subpixels3011R. The display boundary 3015 is determined by the controller 3030.The display boundary 3015 may include a first display boundaryindicating a range in which the first subpixels 3011L are arranged, anda second display boundary indicating a range in which the secondsubpixels 3011R are arranged. This makes it possible to expresssubpixels 3011 that are neither the first subpixels 3011L nor the secondsubpixels 3011R.

The controller 3030 has operation modes between which the orientationsof both the left-eye image and the right-eye image displayed by thedisplay apparatus 3010 are different. The orientations of both theleft-eye image and the right-eye image displayed by the displayapparatus 3010 are also referred to as “image display direction”. It isassumed that the image display direction corresponds to the firstdirection as seen from the user. That is, in the case where the firstdirection is the lateral direction as seen from the user, the imagedisplay direction is assumed to be the lateral direction. In the casewhere the first direction is the longitudinal direction as seen from theuser, the image display direction is assumed to be the longitudinaldirection. The case where the first direction is the longitudinaldirection as seen from the user can be regarded as the case where thesecond direction is the lateral direction as seen from the user.

The controller 3030 has a portrait mode and a landscape mode as theoperation modes. In the case of operating in the portrait mode, thecontroller 3030 sets the image display direction in the displayapparatus 3010 to the lateral direction. In the case where the imagedisplay direction is the lateral direction, the subpixel 3011 isvertically long as seen from the user. In the case of operating in thelandscape mode, the controller 3030 sets the image display direction inthe display apparatus 3010 to the longitudinal direction. In the casewhere the image display direction is the longitudinal direction, thesubpixel 3011 is horizontally long as seen from the user. The portraitmode and the landscape mode are also referred to as “first mode” and“second mode” respectively.

The barrier 3020 includes light transmitting regions 3021 and lightshielding regions 3022, as illustrated in FIG. 47 as an example. The Xaxis and the Y axis in FIG. 47 correspond to the directions of the Xaxis and the Y axis in FIG. 46. The directions of the X axis and the Yaxis rotate with rotation of the display apparatus 3010. Hence, thedirections of the X axis and the Y axis can change with respect to thestructure of the light transmitting regions 3021 and the light shieldingregions 3022.

The light transmitting regions 3021 are parts that transmit lightincident on the barrier 3020. The light transmitting regions 3021 maytransmit light at transmittance of a first sertain value or more. Forexample, the first sertain value may be 100%, or a value close to 100%.The light shielding regions 3022 are parts that shield light incident onthe barrier 3020 so as not to pass through. In other words, the lightshielding regions 3022 shield an image displayed by the displayapparatus 3010. The light shielding region 3022 may shield light attransmittance of a second sertain value or less. For example, the secondsertain value may be 0%, or a value close to 0%.

In FIG. 47, the light transmitting regions 3021 and the light shieldingregions 3022 alternate with each other in the horizontal direction andthe vertical direction. The lines indicating the edges of the lighttransmitting regions 3021 extend in a direction inclined from thevertical direction by a sertain angle θ. The lines indicating the edgesof the light transmitting regions 3021 can also be regarded as the edgesof the light transmitting regions 3021. The sertain angle θ is alsoreferred to as “barrier inclination angle”. 0 may be an angle greaterthan 0 degrees and less than 90 degrees. For example, 0 may bedetermined to satisfy tan θ=a×Hp/b×Vp (a, b: natural numbers). If theedge of the light transmitting region 3021 extends in the Y-axisdirection in FIG. 47 and coincides with the arrangement direction of thesubpixels 3011, moire tends to be recognized in the display image due toerrors contained in the arrangement of the subpixels 3011 and thedimensions of the light transmitting regions 3021. If the edge of thelight transmitting region 3021 extends in the direction having thesertain angle with respect to the Y-axis direction in FIG. 47, moire ishardly recognized in the display image regardless errors contained inthe arrangement of the subpixels 3011 and the dimensions of the lighttransmitting regions 3021.

The barrier 3020 may be composed of a film or a platy member havingtransmittance of less than the second sertain value. In this case, thelight shielding regions 3022 are formed by the film or platy member, andthe light transmitting regions 3021 are formed by openings in the filmor platy member. The film may be made of resin, or made of othermaterial. The platy member may be made of resin, metal, or the like, ormade of other material. The barrier 3020 is not limited to a film or aplaty member, and may be composed of any other type of member. Thebarrier 3020 may be composed of a light shielding substrate. The barrier3020 may be composed of a substrate containing a light shieldingadditive.

The barrier 3020 may be composed of a liquid crystal shutter. The liquidcrystal shutter can control the transmittance of light according to anapplied voltage. The liquid crystal shutter may be made up of pixels,and control the transmittance of light in each pixel. The liquid crystalshutter may form a region with high transmittance of light or a regionwith low transmittance of light, in any shape. In the case where thebarrier 3020 is composed of a liquid crystal shutter, the lighttransmitting regions 3021 may be regions having transmittance of thefirst sertain value or more. In the case where the barrier 3020 iscomposed of a liquid crystal shutter, the light shielding regions 3022may be regions having transmittance of the second sertain value or less.

As illustrated in FIG. 49, it is assumed that the left eye 3005L and theright eye 3005R of the user are located at a optimum viewing distance,denoted by d, from the barrier 3020. The optimum viewing distance isalso referred to as “optical viewing distance (OVD)”. The left eye 3005Land the right eye 3005R can view an image displayed by the displayapparatus 3010 via the barrier 3020. The barrier 3020 includes the lighttransmitting regions 3021 shown as blank and the light shielding regions3022 shown as hatched. The light transmitting regions 3021 and the lightshielding regions 3022 alternate with each other in the X-axisdirection. The pitch with which the light transmitting regions 3021 andthe light shielding regions 3022 alternate is denoted by Bp. Thedistance between the left eye 3005L and the right eye 3005R is donatedby E. The distance from the barrier 3020 to the display apparatus 3010is donated by g.

The display apparatus 3010 includes left-eye visible regions 3013L andright-eye visible regions 3013R visible respectively to the left eye3005L and the right eye 3005R of the user via the light transmittingregions 3021. The display apparatus 3010 includes left-eye lightshielding regions 3014L and right-eye light shielding regions 3014R thatare made not visible respectively to the left eye 3005L and the righteye 3005R of the user by the light shielding regions 3022. The linesindicating the edges of the left-eye visible regions 3013L and theright-eye visible regions 3013R correspond to the lines indicating theedges of the light transmitting regions 3021. The lines indicating theedges of the left-eye light shielding regions 3014L and the right-eyelight shielding regions 3014R correspond to the lines indicating theedges of the light shielding regions 3022. The display boundary 3015 maybe located along the line indicating the edge of each of the left-eyevisible region 3013L and the right-eye visible region 3013R. That is,the display boundary 3015 may be located along the edge of the lighttransmitting region 3021.

In the example in FIG. 49, the following assumption is further made. Thelight transmitting region 3021 and the light shielding region 3022 havethe same width, denoted by Bp/2, in the X-axis direction. In theportrait mode, the ratio of the width of the light transmitting region3021 in the X-axis direction to the width of the light transmittingregion 3021 and the light shielding region 3022 in the X-axis directioncan be regarded as an opening ratio. In the example in FIG. 49, theopening ratio of the barrier 3020 is (Bp/2)/Bp, i.e. 50%. In thelandscape mode, the ratio of the width of the light transmitting region3021 in the X-axis direction to the width of the light transmittingregion 3021 and the light shielding region 3022 in the X-axis directioncan be regarded as an opening ratio.

The pitch with which the left-eye visible regions 3013L and theright-eye visible regions 3013R alternate is denoted by k. The left-eyevisible region 3013L and the right-eye visible region 3013R respectivelyhave widths k_(L) and k_(R) in the X-axis direction. In the portraitmode, the left-eye visible region 3013L includes m subpixels successivealong the horizontal direction. In the portrait mode, the right-eyevisible region 3013R includes m successive subpixels. When tanθ=a×Hp/b×Vp, k satisfies a formula k=2 mHp/b. In the landscape mode, theleft-eye visible region 3013L includes j successive subpixels. In theportrait mode, the right-eye visible region 3013R includes j successivesubpixels. When tan θ=(a×Hp)/(b×Vp)=(a×Vp)/(b×x²×Hp), k satisfies aformula k=2×j×Vp/(b×x²). At the OVD, k_(L) and k_(R) are both expressedas k/2. At the OVD, the left-eye visible regions 3013L and the right-eyevisible regions 3013R alternate without a spacing. At the OVD, theleft-eye visible region 3013L and the right-eye light shielding region3014R overlap with each other. At the OVD, the right-eye visible region3013R and the left-eye light shielding region 3014L overlap with eachother.

The relationships among E, k, d, and g illustrated in FIG. 49 aregeometrically determined. The ratio of E and k/2 is equal to the ratioof d and g. In other words, the relationship of Formula (4-1) holds:

E:k/2=d:g  (4-1).

The relationships among Bp, k, d, and g illustrated in FIG. 49 aregeometrically determined. The ratio of Bp and k is equal to the ratio ofd and (d+g). In other words, the relationship of Formula (4-2) holds:

Bp:k=d:(d+g)  (4-2).

In the case where the light transmitting region 3021 and the lightshielding region 3022 have different widths, k_(L) and k_(R) are eachdifferent from k/2. In the case where the light transmitting region 3021is narrower in width than the light shielding region 3022, k_(L) andk_(R) are each less than k/2. In such a case, the left-eye visibleregion 3013L and the right-eye visible region 3013R are arranged with aspacing. As a result of the left-eye visible region 3013L and theright-eye visible region 3013R being arranged with a spacing, crosstalkcaused by a right-eye image reaching the left eye 3005L or a left-eyeimage reaching the right eye 3005R can be reduced. In the case where thelight transmitting region 3021 is greater in width than the lightshielding region 3022, k_(L) and k_(R) are each greater than k/2. Insuch a case, the left-eye visible region 3013L and the right-eye visibleregion 3013R partially overlap with each other. As a result of theleft-eye visible region 3013L and the right-eye visible region 3013Rpartially overlapping with each other, crosstalk occurs. Here, k alsorepresents the pitch of the left-eye visible region 3013L or theright-eye visible region 3013R. Hereafter, the pitch of the left-eyevisible region 3013L or the right-eye visible region 3013R is alsoreferred to as “visible region pitch”.

In the case where the distance between each of the left eye 3005L andthe right eye 3005R and the barrier 3020 is different from the optimumviewing distance, k_(L) and k_(R) are each not limited to k/2. Forexample, in the case where the distance between each of the left eye3005L and the right eye 3005R and the barrier 3020 is longer than theoptimum viewing distance, k_(L) and k_(R) are each less than k/2. Insuch a case, the left-eye visible region 3013L and the right-eye visibleregion 3013R may be arranged with a spacing. For example, in the casewhere the distance between each of the left eye 3005L and the right eye3005R and the barrier 3020 is shorter than the optimum viewing distance,k_(L) and k_(R) are each greater than k/2. In such a case, the left-eyevisible region 3013L and the right-eye visible region 3013R maypartially overlap with each other.

As illustrated in FIG. 49, the display apparatus 3010 as seen from theleft eye 3005L has the left-eye visible region 3013L and the left-eyelight shielding region 3014L. An image displayed in the left-eye visibleregion 3013L is visible to the left eye 3005L. Meanwhile, an imagedisplayed in the left-eye light shielding region 3014L shielded by thelight shielding region 3022 as indicated by hatching is not visible tothe left eye 3005L. In FIG. 49, the left eye 3005L, the left-eye visibleregion 3013L, and the left-eye light shielding region 3014L can bereplaced with the right eye 3005R, the right-eye visible region 3013R,and the right-eye light shielding region 3014R, respectively. Thedisplay apparatus 3010 as seen from the right eye 3005R has theright-eye visible region 3013R and the right-eye light shielding region3014R. An image displayed in the right-eye visible region 3013R isvisible to the right eye 3005R. Meanwhile, an image displayed in theright-eye light shielding region 3014R shielded by the light shieldingregion 3022 as indicated by hatching is not visible to the right eye3005R.

As illustrated in FIG. 50, in the case where the left eye 3005L moves inthe negative direction of the X axis by d_(HT), the left-eye visibleregion 3013L and the left-eye light shielding region 3014L in thedisplay apparatus 3010 move in the positive direction of the X axis byd_(C). In FIG. 50, the left eye 3005L can be replaced with the right eye3005R. In the case where the right eye 3005R moves in the negativedirection of the X axis by d_(HT), the right-eye visible region 3013Rand the right-eye light shielding region 3014R in the display apparatus3010 move in the positive direction of the X axis by d_(C).

As illustrated in FIG. 51, in the case of operating in the portraitmode, the controller 3030 virtually sets, in a sertain plane, headtracking boundaries 3041 arranged in the X-axis direction based on theshape of the light transmitting region 3021 of the barrier 3020. Thesertain plane is assumed to be parallel to a plane in which the barrier3020 is located, and away from the barrier 3020 by the OVD. The headtracking boundaries 3041 are also referred to as “HT boundaries 3041”.The left eye 3005L or the right eye 3005R is located in any of headtracking regions 3042 defined by the HT boundaries 3041. The headtracking regions 3042 are also referred to as “HT regions 3042”.

The first subpixels 3011L included in the left-eye visible region 3013Lare determined depending on the HT region 3042 in which the left eye3005L is located. For example, in the case where the left eye 3005L islocated in a HT region 3042 a, the left-eye visible region 3013Lindicated by the solid arrow includes subpixels 3011 a, 3011 b, and 3011c. That is, the subpixels 3011 a, 3011 b, and 3011 c are the firstsubpixels 3011L. In the case where the left eye 3005L is located in a HTregion 3042 b, the left-eye visible region 3013L indicated by the dashedarrow includes subpixels 3011 b, 3011 c, and 3011 d. That is, thesubpixels 3011 b, 3011 c, and 3011 d are the first subpixels 3011L.

The interval of the HT boundaries 3041 assumed in the portrait mode isexpressed as I_(1HT)=(Hp×d)/(g×b), using Hp in FIG. 46, etc. and d and gin FIG. 50, etc. In FIG. 51, the left eye 3005L can be replaced with theright eye 3005R. The HT boundaries 3041 are assumed for each of the lefteye 3005L and the right eye 3005R. The HT region 3042 is assumed foreach of the left eye 3005L and the right eye 3005R. The interval of theHT boundaries 3041 assumed in the portrait mode is also referred to as“first interval”.

The interval of the HT boundaries 3041 assumed in the landscape mode isexpressed as I_(2HT)=(Vp×d)/(g×b×x²), using Vp in FIG. 46, etc. and dand g in FIG. 50, etc. The interval of the HT boundaries 3041 assumed inthe landscape mode is also referred to as “second interval”.

In the case where the left-eye visible region 3013L and the right-eyevisible region 3013R move in response to the movement of the left eye3005L and the right eye 3005R, the three-dimensional display system 3001moves the image displayed by the display apparatus 3010 to keepproviding stereoscopic vision to the user. The controller 3030 acquiresthe positions of the left eye 3005L and the right eye 3005R from thedetection apparatus 3040. Based on the positions of the left eye 3005Land the right eye 3005R, the controller 3030 determines the displayboundary 3015 so that the first subpixels 3011L and the second subpixels3011R are respectively located in the left-eye visible region 3013L andthe right-eye visible region 3013R. In other words, when each of theleft eye 3005L and the right eye 3005R passes across the HT boundary3041, the controller 3030 moves the display boundary 3015 in the X-axisdirection by one subpixel. The controller 3030 may move the displayboundary 3015, based on the moving distance of the left eye 3005L andthe right eye 3005R acquired from the detection apparatus 3040. Themoving distance may be detected as the distance from the HT boundary3041 to the left eye 3005L and the right eye 3005R. The controller 3030may move the display boundary 3015, when the moving distance of the lefteye 3005L and the right eye 3005R reaches the first interval.

FIG. 52 illustrates the positions of the left-eye visible region 3013Land the left-eye light shielding region 3014L with respect to thearrangement of the subpixels 3011 as seen from the left eye 3005L. Theleft-eye light shielding region 3014L is indicated as a region withhatching. The left-eye visible region 3013L is indicated as a regionwithout hatching. The arrangement of the subpixels 3011 is dividedbetween the arrangement of the first subpixels 3011L and the arrangementof the second subpixels 3011R by the display boundary 3015. Thearrangement of the first subpixels 3011L is an arrangement in which thesubpixels 3011 of numbers 1 to 6 are included. The arrangement of thesecond subpixels 3011R is an arrangement in which the subpixels 3011 ofnumbers 7 to 12 are included. In FIG. 52, the left eye 3005L, theleft-eye visible region 3013L, and the left-eye light shielding region3014L can be replaced with the right eye 3005R, the right-eye visibleregion 3013R, and the right-eye light shielding region 3014R,respectively. In the case where the left eye 3005L is replaced with theright eye 3005R, the first subpixels 3011L and the second subpixels3011R are replaced with each other.

The left-eye visible region 3013L corresponds to a region visiblethrough the light transmitting region 3021 of the barrier 3020 in FIG.47. The display apparatus 3010 illustrated in FIG. 52 is used in theportrait mode. The display apparatus 3010 includes the first subpixels3011L indicated by hatching, and the second subpixels 3011R separatedfrom the first subpixels 3011L by the display boundary 3015. Thecontroller 3030 determines the position of the display boundary 3015 sothat the first subpixels 3011L are located in the left-eye visibleregion 3013L. The positional relationship between the right-eye visibleregion 3013R and the second subpixels 3011R is the same as thepositional relationship between the left-eye visible region 3013L andthe first subpixels 3011L. In this case, at least part of image lightemitted from the first subpixels 3011L and at least part of image lightemitted from the second subpixels 3011R respectively reach the left eye3005L and the right eye 3005R.

As illustrated in FIG. 51, when the left eye 3005L passes across the HTboundary 3041, the controller 3030 moves the display boundary 3015 inthe X-axis direction by one subpixel 3011. In other words, when the lefteye 3005L moves to the adjacent HT region 3042, the controller 3030moves the display boundary 3015 in the X-axis direction by one subpixel3011. By moving the display boundary 3015 in response to the movement ofthe left eye 3005L, the three-dimensional display system 3001 cancontinuously make the left-eye image visible to the left eye 3005L. Inthe case where the left eye 3005L moves in the positive direction of theX axis, too, the three-dimensional display system 3001 can continuouslymake the left-eye image visible to the left eye 3005L. In the case wherethe right eye 3005R moves in the positive or negative direction of the Xaxis, too, the three-dimensional display system 3001 can continuouslymake the right-eye image visible to the right eye 3005R.

As illustrated in FIG. 50, suppose the left-eye visible region 3013L andthe left-eye light shielding region 3014L move in the positive directionof the X axis by d_(C) in response to the left eye 3005L moving in thenegative direction of the X axis by d_(HT). In such a case, in FIG. 52,too, the left-eye visible region 3013L and the left-eye light shieldingregion 3014L move in the positive direction of the X axis by d_(C). Whend_(C) reaches Hp which is the length of the subpixel 3011 in the X-axisdirection, the controller 3030 may move the display boundary 3015 in theX-axis direction by one subpixel 3011.

The condition for the controller 3030 to move the display boundary 3015may be expressed as the condition that the moving distance of the lefteye 3005L and the right eye 3005R along the X-axis direction reaches acontrol distance, instead of the condition that d_(C) reaches Hp. Themoving distance is assumed to be the distance from the position of theleft eye 3005L and the right eye 3005R when the controller 3030 movedthe display boundary most recently to the position of the left eye 3005Land the right eye 3005R acquired by the controller 3030. The controller3030 sets the control distance in the portrait mode depending on thearrangement of the subpixels 3011. The control distance in the portraitmode is expressed as D_(1HT)=(Hp×d)/(g×b), using d and g in FIG. 50. Thecontrol distance in the portrait mode is also referred to as “firstdistance”. That is, when the moving distance reaches the first distance,the controller 3030 moves the display boundary 3015 in the X-axisdirection by one subpixel 3011.

In the display apparatus 3010 illustrated in FIG. 52 described above,the image display direction is the lateral direction. In the displayapparatus 3010 illustrated in FIG. 53, on the other hand, the imagedisplay direction is the longitudinal direction. In detail, with respectto the display apparatus 3010 illustrated in FIG. 52, the displayapparatus 3010 illustrated in FIG. 53 is rotated 90 degreescounterclockwise as seen from the positive side of the Z axis, in aplane along the X-axis direction and the Y-axis direction.

In FIG. 53, the barrier 3020 is not rotated relative to the user. Thatis, with respect to the barrier 3020, too, the display apparatus 3010 isrotated 90 degrees counterclockwise as seen from the positive side ofthe Z axis. Since the barrier 3020 is not rotated, the arrangement ofthe subpixels 3011 is rotated 90 degrees counterclockwise as seen fromthe positive side of the Z axis with respect to the left-eye visibleregion 3013L. In other words, the barrier 3020 is rotated 90 degreesclockwise in a plane along the X-axis direction and the Y-axis directionwith respect to the display apparatus 3010.

FIG. 53 illustrates the positions of the left-eye visible region 3013Land the left-eye light shielding region 3014L with respect to thearrangement of the subpixels 3011 as seen from the left eye 3005L. Thearrangement of the subpixels 3011 includes the arrangement of the firstsubpixels 3011L and the arrangement of the second subpixels 3011R. Thearrangement of the first subpixels 3011L is an arrangement of subpixels3011 with hatching. The arrangement of the second subpixels 3011R is anarrangement of subpixels 3011 without hatching. The first subpixels3011L and the second subpixels 3011R are separated by the displayboundary 3015. In FIG. 53, part of the first subpixel 3011L has numbers19 to 36, and part of the second subpixels 3011R has numbers 1 to 18.

The display apparatus 3010 illustrated in FIG. 53 is used in thelandscape mode. The display apparatus 3010 includes the first subpixels3011L and the second subpixels 3011R, as in FIG. 52. At least part ofimage light emitted from the first subpixels 3011L and at least part ofimage light emitted from the second subpixels 3011R respectively reachthe left eye 3005L and the right eye 3005R. The aspect ratio of thesubpixel 3011 in FIG. 53 is the reciprocal of the aspect ratio of thesubpixel 3011 in FIG. 52.

In FIG. 53, suppose the left eye 3005L and the right eye 3005R move inthe positive or negative direction of the Y axis. When the left eye3005L and the right eye 3005R pass across the HT boundaries 3041arranged at the second interval in the Y-axis direction, the controller3030 operating in the landscape mode moves the display boundary 3015 inthe Y-axis direction by one subpixel 3011.

The second interval is expressed as I_(2HT)=(Vp×d)/(g×b×x²), asmentioned above. The ratio of the second interval to the first intervalis expressed as Vp/Hp (=x). In other words, the ratio of the secondinterval to the first interval is the ratio of the length of thesubpixel 3011 in the second direction to the length of the subpixel 3011in the first direction. Even in the case where the aspect ratio of thesubpixel 3011 is the reciprocal depending on the operation mode, thecontroller 3030 can easily change the interval of the HT boundary 3041depending on the aspect ratio.

The controller 3030 may move the display boundary 3015 depending on themoving distance of the left eye 3005L and the right eye 3005R along theY-axis direction, as in the operation in the portrait mode illustratedin FIG. 52. The controller 3030 may set a control distance in thelandscape mode. The control distance in the landscape mode is expressedas D_(2HT)=(Vp×d)/(g×b×x²). The control distance in the landscape modeis also referred to as “second distance”. That is, when the movingdistance reaches the second distance, the controller 3030 moves thedisplay boundary 3015 in the Y-axis direction by one subpixel 3011. Inthe landscape mode, too, the three-dimensional display system 3001 cancontinuously make the left-eye image and the right-eye image visible tothe left eye 3005L and the right eye 3005R respectively, as in theportrait mode.

The ratio of the second distance to the first distance is expressed asVp/Hp (=x). In other words, the ratio of the second distance to thefirst distance is the ratio of the length of the subpixel 3011 in thesecond direction to the length of the subpixel 3011 in the firstdirection. Even in the case where the aspect ratio of the subpixel 3011is the reciprocal depending on the operation mode, the controller 3030can easily change the control distance depending on the aspect ratio.

In the portrait mode illustrated in FIG. 52 and the landscape modeillustrated in FIG. 53, the barrier 3020 may have a common structureregardless of which mode the arrangement of the subpixels 3011corresponds to. In detail, the same structure of the light transmittingregion 3021 and the light shielding region 3022 may be used in bothmodes. For example, the barrier 3020 having the same ratio of the widthof the light transmitting region 3021 and the width of the lightshielding region 3022, pitch of repeating the light transmitting region3021 and the light shielding region 3022, barrier inclination angle, andthe like may be used.

The three-dimensional display system 3001 according to this embodimentcan provide stereoscopic vision to the user using the barrier 3020 ofthe same structure, even in the case where the display apparatus 3010 isrotated 90 degrees as seen from the user and as a result the aspectratio of the subpixel 3011 becomes the reciprocal. In the case where thebarrier 3020 is composed of a film or a plate member, the barrier 3020of the same structure can be commonly used in the modes, thus enablinguse of a common member. In the case where the barrier 3020 is composedof a liquid crystal shutter, the pattern for controlling thetransmittance of each pixel in the liquid crystal shutter is common, sothat the storage capacity for pattern data can be saved. In addition,the control circuitry of the liquid crystal shutter can be simplified.This contributes to lower costs.

The controller 3030 may move the display boundary 3015 in the X-axisdirection or the Y-axis direction not by one subpixel but by csubpixels. Here, c is a natural number of 2 or more. c may be the numberof subpixels 3011 constituting the pixel 3012. For example, c may be 3.In this case, the control distance corresponding to c=3 is three timesthe control distance corresponding to c=1. When the moving distancereaches the control distance, the controller 3030 moves the displayboundary 3015 in the X-axis direction by three subpixels 3011. This cansimplify image display control. In the case where three subpixels 3011display the colors of R, G, and B, color display by one pixel 3012 canbe controlled as a whole. c denotes a unit number for switching displayof subpixels 3011 in HT control. The unit number for switching displayof subpixels 3011 in HT control is also referred to as “HT controlunit”.

It is assumed that, in the barrier 3020, the sertain angle θ between theedge of the light transmitting region 3021 and the direction orthogonalto the vertical direction is determined to satisfy tan θ=a×Hp/b×Vp (a,b: natural numbers). By applying x=Vp/Hp, the formula satisfied by θ isexpressed as tan θ=a/b×x.

In the portrait mode, k denoting the visible region pitch is expressedby the following Formula (4-3):

k=n×Hp/b  (4-3).

The longitudinal length and the lateral length of the subpixel 3011 inthe landscape mode are respectively Hp and Vp, i.e. the reverse of theportrait mode. The direction indicated by the barrier inclination anglecorresponds to a direction represented by a component having a lengthcorresponding to a subpixels 3011 and a component having a lengthcorresponding to (b×x×x) subpixels 3011 respectively in the horizontaldirection and the vertical direction. In this case, the formulasatisfied by θ is the following Formula (4-4):

tan θ=a×Vp/(b×x×x×Hp)  (4-4).

Suppose, in the landscape mode, a pair of a right-eye image and aleft-eye image are displayed in p successive subpixels 3011. Bysubstituting, in Formula (4-3), n by p, Hp by Vp, and b by b×x×x, kdenoting the visible region pitch is expressed by the following Formula(4-5):

k=p×Vp/(b×x×x)=p×Hp/(b×x)  (4-5).

As a result of the visible region pitch k being the same value in theportrait mode and the landscape mode, the OVD can be the same. In thecase where the OVD is the same, the barrier 3020 can be used in common.In the case where k is the same value in both modes, n×x=p holds basedon Formulas (4-3) and (4-5). In other words, in the case where a pair ofa right-eye image and a left-eye image are displayed in n successivesubpixels 3011 in the portrait mode, a pair of a right-eye image and aleft-eye image are displayed in n×x successive subpixels 3011 in thelandscape mode.

It is assumed that the left-eye visible region 3013L and the left-eyelight shielding region 3014L illustrated in FIG. 52 are formed by thebarrier 3020 having a barrier inclination angle calculated with a=b=1and x=3.

At least part of the first subpixels 3011L has numbers 1 to 6. At leastpart of the second subpixels 3011R has numbers 7 to 12. Thus, it isassumed that a pair of a right-eye image and a left-eye image aredisplayed in 12 (n=12) successive subpixels 3011. In this case, thevisible region pitch is expressed as k=12×Hp, based on Formula (4-3).

The left-eye visible region 3013L and the left-eye light shieldingregion 3014L illustrated in FIG. 53 are similar to the left-eye visibleregion 3013L and the left-eye light shielding region 3014L illustratedin FIG. 52. At least part of the second subpixels 3011R has numbers 1 to18. At least part of the first subpixels 3011L has numbers 19 to 36.Thus, given that n=12 in the portrait mode, a pair of a right-eye imageand a left-eye image are displayed in 36 (p=n×x=36) successive subpixels3011 in the landscape mode.

In the case where a pair of a right-eye image and a left-eye image aredisplayed in n successive subpixels 3011 in the portrait mode, crosstalkcan be reduced if n satisfies at least the following Formula (4-6):

n≥2×(a+b−1)  (4-6).

In the landscape mode, on the other hand, a pair of a right-eye imageand a left-eye image are displayed in n×x successive subpixels 3011.

Substituting, in Formula (4-6), n by n×x and b by b×x×x yields thefollowing Formula (4-7). In the landscape mode, crosstalk can be reducedif n satisfies at least the following Formula (4-7):

n≥2×(a+b×x×x−1)/x  (4-7).

It is assumed that the barrier inclination angle is determined tosatisfy tan θ=x×Hp/Vp=1. In this case, a/b=x, and 0=45 degrees. Thebarrier inclination angle is 45 degrees both in the case where thedisplay apparatus 3010 is used in the portrait mode and in the casewhere the display apparatus 3010 is used in the landscape mode.

For example, it is assumed that, in the case where x=3, image display iscontrolled with the HT control unit being 3 in the portrait mode. Inthis case, image display is controlled with the HT control unit being 3in the landscape mode, too. Thus, in the case where the HT control unitin the portrait mode is c, the HT control unit in the landscape mode isalso c.

With a barrier inclination angle of 45 degrees, image display can becontrolled using the same HT control unit in the portrait mode and thelandscape mode. This eases image display control.

The three-dimensional display system 3001 according to this embodimentcan provide stereoscopic vision to the user simply by changing thecontrol distance depending on the aspect ratio of the subpixel 3011,even in the case where the display apparatus 3010 is used in a state inwhich the aspect ratio of the subpixel 3011 is the reciprocal.Computation required to change the control distance depending on theaspect ratio of the subpixel 3011 is, for example, less than computationrequired to change the shape of the display boundary 3015. The structureof the controller 3030 can therefore be simplified. This contributes tolower costs.

In the example in FIG. 49, the light transmitting region 3021 and thelight shielding region 3022 have the same width in the X-axis direction.However, the present disclosure is not limited to such. The lighttransmitting region 3021 and the light shielding region 3022 may havedifferent widths in the X-axis direction. The ratio of the lighttransmitting region 3021 and the light shielding region 3022 may bedifferent between the portrait mode and the landscape mode. The openingratio of the barrier 3020 may be different between the portrait mode andthe landscape mode. For example, the opening ratio in the landscape modemay be less than the opening ratio in the portrait mode. The inclinationangle of the barrier 3020 may be the same in the portrait mode and thelandscape mode. Computation required to change the position of thedisplay boundary 3015 is, for example, less than computation required tochange the shape of the display boundary 3015. In the case where thesubpixel of the display apparatus 3010 is longer in the Y-axisdirection, crosstalk is greater in the landscape mode than in theportrait mode. As a result of the opening ratio in the landscape modebeing less than the opening ratio in the portrait mode, thethree-dimensional display system 3001 can reduce crosstalk by simplecontrol.

In the case where the opening ratio of the barrier 3020 is differentbetween the portrait mode and the landscape mode, the controller 3030may change the luminance of the light source device between the portraitmode and the landscape mode. The controller 3030 may set the luminancein the landscape mode to be higher than the luminance in the portraitmode.

The three-dimensional display system 3001 may be equipped in a head updisplay 3100, as illustrated in FIG. 54. The head up display 3100 can beabbreviated as “HUD 3100”. The HUD 3100 is also referred to as “head updisplay system”. The HUD 3100 includes the three-dimensional displaysystem 3001, an optical member 3110, and a projection target member 3120having a projection target surface 3130. The HUD 3100 causes image lightemitted from the three-dimensional display system 3001 to reach theprojection target member 3120 via the optical member 3110. The HUD 3100causes the image light reflected off the projection target member 3120to reach the left eye 3005L and the right eye 3005R of the user. Thus,the HUD 3100 causes the image light to travel from the three-dimensionaldisplay system 3001 to the left eye 3005L and the right eye 3005R of theuser along an optical path 3140 indicated by dashed lines. The user canview the image light that has reached along the optical path 3140, asthe virtual image 3150. The three-dimensional display system 3001 canprovide stereoscopic vision according to the movement of the user, bycontrolling the display depending on the positions of the left eye 3005Land the right eye 3005R of the user detected by the detection apparatus3040.

The HUD 3100 and the three-dimensional display system 3001 may beequipped in a mobile object. The HUD 3100 and the three-dimensionaldisplay system 3001 have part of their structure shared with anotherapparatus or component included in the mobile object. For example, themobile object may use a windshield as part of the HUD 3100 and thethree-dimensional display system 3001. In the case where part of thestructure is shared with another apparatus or component included in themobile object, the other structure can be referred to as “HUD module” or“three-dimensional display component”. The three-dimensional displaysystem 3001 and the display apparatus 3010 may be equipped in a mobileobject.

The presently disclosed structures are not limited to the foregoingembodiments, and various modifications and changes are possible. Forexample, the functions, etc. included in the components, the steps, etc.may be rearranged without logical inconsistency, and components, etc.may be combined into one component, etc. and a component, etc. may bedivided into components, etc.

The drawings used to describe the presently disclosed structures areschematic, and the dimensional ratios, etc. in the drawings do notnecessarily coincide with actual dimensional ratios, etc.

Terms such as “first” and “second” in the present disclosure areidentifiers for distinguishing components. Components distinguished byterms such as “first” and “second” in the present disclosure may havetheir numbers interchanged with each other. For example, the identifier“first” of the “first direction” and the identifier “second” of the“second direction” may be interchanged with each other. The identifiersare replaced with each other simultaneously. The components aredistinguishable even after their identifiers are interchanged. Theidentifiers may be omitted. Components from which identifiers areomitted are distinguished by reference signs. Description of identifierssuch as “first” and “second” in the present disclosure alone should notbe used for interpretation of order of components or reasoning based onone identifier being smaller than another identifier.

REFERENCE SIGNS LIST

-   -   1 three-dimensional display system    -   2 detection apparatus    -   3 three-dimensional display apparatus    -   4 irradiation unit    -   5 display panel (display apparatus)    -   6 parallax barrier (optical element)    -   7 controller    -   8 mobile object    -   9 lenticular lens (optical element)    -   10 cylindrical lens    -   11 subpixel    -   11L first subpixel    -   11R second subpixel    -   12 pixel    -   15 display boundary    -   51 display surface    -   52 left-eye visible region    -   53 left-eye light shielding region    -   61 light shielding region    -   62 light transmitting region    -   100 head up display    -   110 optical member    -   120 projection target member    -   130 projection target surface    -   140 optical path    -   150 virtual image    -   1001 three-dimensional display system    -   1002 detection apparatus    -   1003 three-dimensional display apparatus    -   1004 irradiation unit    -   1005 display panel    -   1006 parallax barrier    -   1007 controller    -   1008 mobile object    -   1009 lenticular lens    -   1010 cylindrical lens    -   1051 display surface    -   1052 black matrix    -   1052 a first black line    -   1052 b second black line    -   1053 visible region    -   1054 light shielding region    -   1061 light shielding surface    -   1062 open region    -   1100 head up display system    -   1110 optical member    -   1120 projection target member    -   1130 projection target surface    -   1140 optical path    -   1150 virtual image    -   2001 three-dimensional display system    -   2005L left eye    -   2005R right eye    -   2010 display apparatus    -   2010 a display surface    -   2011 subpixel    -   2011L first subpixel    -   2011R second subpixel    -   2012 pixel    -   2013L left-eye visible region    -   2013R right-eye visible region    -   2014L left-eye light shielding region    -   2014R right-eye light shielding region    -   2015 display boundary    -   2016 right-eye image same boundary    -   2017 (2017 a, 2017 b, 2017 c) right-eye image same region    -   2020 barrier    -   2021 light transmitting region    -   2022 light shielding region    -   2030 controller    -   2040 detection apparatus    -   2041 head tracking boundary    -   2042 (2042 a, 2042 b) head tracking region    -   2051 dot region    -   2052 control boundary    -   2053 control region    -   2054 optimum viewing distance plane    -   2100 HUD    -   2110 optical member    -   2120 projection target member    -   2130 projection target surface    -   2140 optical path    -   2150 virtual image    -   3001 three-dimensional display system    -   3005L left eye    -   3005R right eye    -   3010 display apparatus    -   3011 subpixel    -   3011L first subpixel    -   3011R second subpixel    -   3012 pixel    -   3013L left-eye visible region    -   3013R right-eye visible region    -   3014L left-eye light shielding region    -   3014R right-eye light shielding region    -   3015 display boundary    -   3020 barrier    -   3021 light transmitting region    -   3022 light shielding region    -   3030 controller    -   3040 detection apparatus    -   3041 head tracking boundary    -   3042 (3042 a, 3042 b) head tracking region    -   3100 HUD    -   3110 optical member    -   3120 projection target member    -   3130 projection target surface    -   3140 optical path    -   3150 virtual image

1. A three-dimensional display apparatus comprising: a display apparatushaving a display surface including subpixels arranged in a grid in afirst direction, and a second direction, and configured to display aleft-eye image and a right-eye image respectively in first subpixels andsecond subpixels separated by display boundaries passing alongboundaries between the subpixels; and an optical element configured toselectively transmit at least part of the left-eye image in a directionof an optical path toward a left eye of the user, and selectivelytransmit at least part of the right-eye image in a direction of anoptical path toward a right eye of the user, wherein when an arrangementin the first direction of the grid formed by the subpixels is a row andan arrangement in the second direction of the grid is a column, a firstsertain number of the first subpixels and of the second subpixels areeach successively arranged in each column, a region in which the firstsubpixels are arranged and a region in which the second subpixels arearranged are displaced from each other in the second direction by asecond sertain number between two adjacent columns, and the firstsertain number is greater than the second sertain number and is not amultiple of the second sertain number.
 2. The three-dimensional displayapparatus according to claim 1, wherein each of the subpixels is longerin the first direction than in the second direction.
 3. Thethree-dimensional display apparatus according to claim 1, wherein theoptical element is located at a sertain distance away from the displaysurface, includes a light shielding region and a light transmittingregion arranged in a slit shape, and is configured to cause the firstsubpixels to be visible to the left eye of the user and the secondsubpixels to be visible to the right eye of the user.
 4. Thethree-dimensional display apparatus according to claim 3, wherein apitch in the first direction of the light shielding region and the lighttransmitting region on the display surface viewed by the user isapproximately equal to a value obtained by multiplying, by a pitch ofthe subpixel in the first direction, a quotient obtained by dividingtwice the first sertain number by the second sertain number.
 5. Thethree-dimensional display apparatus according to claim 1, wherein theoptical element is a lenticular lens located at a sertain distance awayfrom the display surface, and is configured to cause the first subpixelsto be visible to the left eye of the user and the second subpixels to bevisible to the right eye of the user.
 6. The three-dimensional displayapparatus according to claim 1, comprising an optical system configuredto project image light emitted from the display surface and transmittedthrough the optical element so as to form a virtual image in a field ofview of the user.
 7. A three-dimensional display system comprising: adisplay apparatus having a display surface including subpixels arrangedin a grid in a first direction corresponding to a direction in whichparallax is provided to eyes of a user and a second directionapproximately orthogonal to the first direction, and configured todisplay a left-eye image and a right-eye image respectively in firstsubpixels and second subpixels separated by display boundaries passingalong boundaries between the subpixels; an optical element configured toselectively transmit at least part of the left-eye image in a directionof an optical path toward a left eye of the user, and selectivelytransmit at least part of the right-eye image in a direction of anoptical path toward a right eye of the user; a detection apparatusconfigured to detect positions of the left eye and the right eye of theuser; and a controller configured to move the display boundaries, basedon the positions of the left eye and the right eye of the user detectedby the detection apparatus, wherein when an arrangement in the firstdirection of the grid formed by the subpixels is a row and anarrangement in the second direction of the grid is a column, a firstsertain number of the first subpixels and of the second subpixels areeach successively arranged in each column, a region in which the firstsubpixels are arranged and a region in which the second subpixels arearranged are displaced from each other in the second direction by asecond sertain number between two adjacent columns, and the firstsertain number is greater than the second sertain number and is not amultiple of the second sertain number.
 8. A head up display comprising:a display apparatus having a display surface including subpixelsarranged in a grid in a first direction corresponding to a direction inwhich parallax is provided to eyes of a user and a second directionapproximately orthogonal to the first direction, and configured todisplay a left-eye image and a right-eye image respectively in firstsubpixels and second subpixels separated by display boundaries passingalong boundaries between the subpixels; an optical element configured toselectively transmit at least part of the left-eye image in a directionof an optical path toward a left eye of the user, and selectivelytransmit at least part of the right-eye image in a direction of anoptical path toward a right eye of the user; a detection apparatusconfigured to detect positions of the left eye and the right eye of theuser; a controller configured to move the display boundaries, based onthe positions of the left eye and the right eye of the user detected bythe detection apparatus; and an optical system configured to projectimage light emitted from the display surface and transmitted through theoptical element so as to form a virtual image in a field of view of theuser, wherein when an arrangement in the first direction of the gridformed by the subpixels is a row and an arrangement in the seconddirection of the grid is a column, a first sertain number of the firstsubpixels and of the second subpixels are each successively arranged ineach column, a region in which the first subpixels are arranged and aregion in which the second subpixels are arranged are displaced fromeach other in the second direction by a second sertain number betweentwo adjacent columns, and the first sertain number is greater than thesecond sertain number and is not a multiple of the second sertainnumber.
 9. A three-dimensional display apparatus design method for athree-dimensional display apparatus including: a display apparatushaving a display surface including subpixels arranged in a grid in afirst direction corresponding to a direction in which parallax isprovided to eyes of a user and a second direction approximatelyorthogonal to the first direction, and configured to display a left-eyeimage and a right-eye image respectively in first subpixels and secondsubpixels separated by display boundaries passing along boundariesbetween the subpixels; and an optical element configured to selectivelytransmit at least part of the left-eye image in a direction of anoptical path toward a left eye of the user, and selectively transmit atleast part of the right-eye image in a direction of an optical pathtoward a right eye of the user, the three-dimensional display apparatusdesign method comprising: determining a optimum viewing distance;determining an image pitch that is a pitch in the first direction withwhich the left-eye image and the right-eye image are displayed, based onthe optimum viewing distance; determining a first sertain number and asecond sertain number based on the image pitch, the first sertain numberbeing greater than the second predetermined number; and determining anarrangement method of the first subpixels and the second subpixels and ashape of the optical element based on the first sertain number and thesecond sertain number, wherein when an arrangement in the firstdirection of the grid formed by the subpixels is a row and anarrangement in the second direction of the grid is a column, the firstsertain number of the first subpixels and of the second subpixels areeach successively arranged in each column, and a region in which thefirst subpixels are arranged and a region in which the second subpixelsare arranged are displaced from each other in the second direction bythe second sertain number between two adjacent columns. 10.-42.(canceled)
 43. The three-dimensional display apparatus according toclaim 1, wherein the first direction is corresponding to a direction, inwhich parallax is provided to eyes of a user, and the second directionis approximately orthogonal to the first direction.
 44. Thethree-dimensional display system according to claim 7, wherein the firstdirection is corresponding to a direction, in which parallax is providedto eyes of a user, and the second direction is approximately orthogonalto the first direction.
 45. The head up display according to claim 8,wherein the first direction is corresponding to a direction, in whichparallax is provided to eyes of a user, and the second direction isapproximately orthogonal to the first direction.
 46. Thethree-dimensional display apparatus design method according to claim 9,wherein the first direction is corresponding to a direction, in whichparallax is provided to eyes of a user, and the second direction isapproximately orthogonal to the first direction.